Estimation and reduction of random noise in mass anomaly time-series from satellite gravity data by minimization of month-to-month year-to-year double differences

Abstract

We propose a technique to regularize a GRACE-based mass-anomaly time-series in order to (i) to quantify the Standard Deviation (SD) of random noise in the data, and (ii) to reduce the level of that noise. The proposed regularization functional minimizes the Month-to-month Year-toyear Double Differences (MYDD) of mass anomalies. As such, it does not introduce any bias in the linear trend and the annual component, two of the most common features in GRACE-based mass anomaly time-series. In the context of hydrological and ice sheet studies, the proposed regularization functional can be interpreted as an assumption about the stationarity of climatological conditions. The optimal regularization parameter and noise SD are obtained using Variance Component Estimation. To demonstrate the performance of the proposed technique, we apply it to both synthetic and real data. In the latter case, two geographic areas are considered: the Tonlé Sap basin in Cambodia and Greenland. We show that random noise in the data can be efficiently (1.5-2 times) mitigated in this way, whereas no noticeable bias is introduced. We also discuss various findings that can be made on the basis of the estimated noise SD. We show, among others, that knowledge of noise SD facilitates the analysis of differences between GRACE-based and alternative estimates of mass variations. Moreover, inaccuracies in the latter can also be quantified in this way. For instance, we find that noise in the surface mass anomalies in Greenland estimated using the Regional Climate Model RACMO2.3 is at the level of 2-6 cm equivalent water heights. Furthermore, we find that this noise shows a clear correlation with the amplitude of annual mass variations: it is lowest in the northwest of Greenland and largest in the south. We attribute this noise to limitations in the modelling of the meltwater accumulation and runoff .

Using GRACE to Explain Variations in the Earth's Oblateness

“…According to the method proposed by Ditmar et al (2018), the error in the FPA solution (approximately ±1.0 × 10 −10 ) is comparable to that of the SLR solution (Cheng et al, 2013). According to the method proposed by Ditmar et al (2018), the error in the FPA solution (approximately ±1.0 × 10 −10 ) is comparable to that of the SLR solution (Cheng et al, 2013).…”

“…Note that the SLR solution is represented by a gray band where the upper and lower bounds are defined by the ± 2 ( denotes the mean values), respectively. The same is also applied to the GRACE-OBP solution, where the uncertainty ( = 1.13 × 10 −10 ) is calculated based on Ditmar et al (2018). The error bars are also shown for the FPA solution.…”

“…A plot showing the estimates based on the CSR RL05 can be found in the supporting information ( Figure S9). We calculate uncertainties of the FPA solution using the method developed by Ditmar et al (2018). The 1 interval (1.01 × 10 −10 ) is shown with black error bars: it is slightly larger than the RL05 version ( = 0.97 × 10 −10 ) and comparable with the SLR uncertainty, which has a mean value of 0.83 × 10 −10 (computed from the uncertainties shown in the data file ftp://ftp.csr.utexas.edu/pub/slr/degree_2/RL06/C20_RL06_2018_04.txt).…”

Improvements in the Monthly Gravity Field Solutions Through Modeling the Colored Noise in the GRACE Data

“…The resulting value of σ d is used as an estimate of standard deviation (SD) of random noise in the considered data. For a more extended presentation of this approach, the reader is referred to Ditmar et al ().…”

“…The resulting value of σ d is used as an estimate of standard deviation (SD) of random noise in the considered data. For a more extended presentation of this approach, the reader is referred to Ditmar et al (2018). Figure 6 displays geographical maps of the derived trends and periodic annual signals in mass changes from the unfiltered solutions.…”