GRACE Level-2数据的RTS状态平滑

RTS state smoothing of GRACE Level-2 data

GRACE Level-2球谐系数反演得到的全球地表质量变化存在明显的南北条带噪声,严重影响区域地表质量异常估计的精度。DDK滤波引入信号协方差矩阵和正则化因子,能较好地削弱条带误差,同时保留更多的真实信号。采用状态空间模型表示球谐系数在相邻月份之间的联系,进而通过卡尔曼滤波实现去条带,即为状态空间DDK滤波方法(SS-DDK)。本文提出的SS-DDK方法状态向量只包含球谐系数,反映条带误差统计信息的协方差矩阵被用作状态空间模型中观测噪声协方差矩阵,采用幂律模型设计过程噪声协方差矩阵,通过迭代法求解方差分量因子,最后输出RTS平滑解代替卡尔曼滤波解作为最终数据处理结果。结果表明,在全球范围内,SS-DDK结果不存在明显的条带误差;计算各约束解与mascon解质量异常差异的均方根(RMSD),SS-DDK的RMSD为10.36 cm,小于任意一种DDK滤波。对比五大区域135个月所有约束解的等效水柱高、年振幅及RMSD发现,在格陵兰岛,SS-DDK所导致的信号失真更少,仅为49.8 cm;在其他区域,SS-DDK的去条带和保留信号的能力与DDK3—5滤波有不同程度的相似,在某些时段优于所有DDK滤波。对估计结果进行不确定性分析,SS-DDK解全球的不确定性大小为2.20 cm,其在所选区域的不确定性大小介于DDK2和DDK3之间。对比大地水准面阶误差的结果说明,SS-DDK解的噪声水平低于DDK4—8,保留信号能力与DDK2—3相当。增添仿真试验进一步说明SS-DDK在去条带和保留信号方面具有较好的性能。

The global surface mass variation obtained by using the unconstrained gravity recovery and climate experiment(GRACE)Level-2 spherical harmonic coefficient inversion has obvious north-south striping noise,which seriously affects the accuracy of regional surface mass anomaly estimation.The decorrelation and denoising kernel(DDK)filter introduced signal covariance matrix and regularization factor to deal with spherical harmonic coefficients to obtain spatial constrained solutions in order to better weaken striping errors and retain more real geophysical signals.DDK filtering ignores the correlation of spherical harmonic coefficients in time,and uses the state space(SS)model to represent the relation between spherical harmonic coefficients in adjacent months,and then realizes noise reduction through Kalman filtering,which is the state space DDK filtering method(SS-DDK).In the SS-DDK method proposed in this paper,the state vector only contains spherical harmonic coefficients,and the covariance matrix reflecting the strip error statistics is used as the observation noise covariance matrix in the state space model.The power law model is used to design the process noise covariance matrix,and the variance component factors are solved by iterative method.Finally,the RTS smooth solution was output instead of the Kalman filter solution as the final data processing result.The results show that there is no significant striping error in SS-DDK results worldwide.The root mean square deviation(RMSD)of the abnormal quality difference between each constraint solution and mascon solution was calculated.The RMSD of SS-DDK is 10.36 cm,which is smaller than that of any DDK filter.By comparing the equivalent water column height,annual amplitude and RMSD of all constraint solutions in the five regions for 135 months,it is found that in Greenland,the signal distortion caused by SS-DDK is less,only 49.8 cm.In other regions,SS-DDK's striping and retention capabilities are somewhat similar to those of DDK3—5 filtering,and superior to all DDK filtering in some time periods.An uncertainty analysis of the estimation results shows that the global uncertainty size of the SS-DDK solution is 2.20 cm,which is between DDK2 and DDK3 in the selected regions.From the point of view of geoid degree error,the noise level of SS-DDK solution is lower than that of DDK4—8,and the signal retention ability is comparable to DDK2—3.The addition of simulation experiments further demonstrates the good performance of SS-DDK in terms of de-striping and signal retention.