Inferring Missing Solutions within and between GRACE and GRACE-FO Missions
Authors: Rateb Ashraf , R. Scanlon Bridget , Sun Alexander , Save Himanshu 
Published: March 2022

&lt;p&gt;Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission and its successor (Follow-On) (FO) monitored the temporal variations of Earth's gravity field at monthly timescales and provided data to assess natural and anthropogenic drivers of water storage variability. Yet, missing solutions within and between the missions disrupt the continuity of observations and weaken the interpretation of changes in the Earth's mass movements. Most approaches used to impute the missing solutions rely on external data, either from a separate satellite (e.g., SWARM), or Global Positioning System, or adopting hydrological and climate data within statistical learning frameworks. Such approaches jeopardize the uniqueness of GRACE-GRACE FO observations and introduce a level of uncertainty from the external data. In addition, the missing solutions are commonly imputed over land only, but not for the ocean or the ice sheets. Further, the reconstructed signals are recovered as single value without uncertainty estimates.&lt;/p&gt;&lt;p&gt;The objective of this research was to impute missing solutions within and between the two missions using GRACE data alone within a Bayesian framework. We decomposed the geophysical signal in GRACE-GRACE (FO) data into its temporal components and modeled each component to infer their posterior distribution over monitored and missing dates. The geophysical signal in GRACE missions is structured as a trend, interannual, annual, and semi-annual cycles. Using informative priors on the ranges of signal intercepts, slopes, frequencies, variability, and amplitudes and assuming these parameters follow a normal distribution, we approximated the posterior distribution of each component using four chains of Markov Chain Monte Carlo. We used 4000 samples for each chain &amp;#160;(518x10&lt;sup&gt;6&lt;/sup&gt; iterations globally) and ensured equilibrium sampling and posteriors convergence over the parameters. Medians of posterior distributions of all components were then added back to reconstruct the signal, and uncertainty was derived at 95% credible interval. Finally, to maintain the same level of variability as the original data, model residuals were added back over the monitored times only. We reconstructed 229 solutions for the period 04/2002 -04/2020 using 188&amp;#160; mascons solutions released by the University of Texas at Austin, Center for Space Research at a 1-degree scale and for 30 hydrological basins.&amp;#160;&amp;#160;&lt;/p&gt;&lt;p&gt;Results reveal that the reconstructed data explain most of the total variability in original data with median &lt;sup&gt;r-square&lt;/sup&gt; of 0.99 at basin scale. However, the explained variability decreases to median 78% at grid scale. We noticed that model performance is good for most of the land/ocean and ice sheet surfaces with &lt;sup&gt;r-square &lt;/sup&gt;over 0.8, except in regions where the signal was already weak (e.g., Sahara desert) or where sub-annual fluctuations mostly dominate the signal (e.g., southern Indian and Pacific Oceans and northern Atlantic Ocean). We attribute this low performance to the model parameterizations. However, the variability in GRACE data is maintained in these regions when the residuals are added back. The implemented framework does not rely on or require external information and uses GRACE data only. The predictive posterior distributions can be adopted for nowcasting and integrated into near-real-time applications (e.g., data assimilation), which minimizes the GRACE data latency.&amp;#160;&amp;#160;&lt;/p&gt;