@MISC\{IMM2018-07120,
    author       = "J. G. Jansen",
    title        = "An analysis of the Global Gravitational Data from the {GRACE} satellites",
    year         = "2018",
    publisher    = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Richard Petersens Plads, Building 324, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    note         = "Supervised by Allan Aasbjerg Nielsen, alan@dtu.dk (Associate Professor, {DTU} Compute), and Ole Baltazar Andersen",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "In 2002 {NASA} launched the {GRACE} (Gravity Recovery and Climate Experiment) to monitor changes in Earth’s gravity on a global scale.  This proved to be the most effective method yet for monitoring displacements and movement of water over short time-scales,  with very high accuracy.
The goal of this thesis is to analyze the global gravitational data collected by the {GRACE} twin-satellites,  by using regression and principal component analysis and interpreting the results. The open source processed grid data,  expressed in an Equivalent Water Height format,  was provided by the people of {CNES}/{GRGS,} in France.
During this thesis,  an analysis was made first on the entire globe,  summing up the interesting parts in regards to its distribution of water mass, and then in various regions where substantial changes of water masses are being observed.  A full regression model was made for each longitude and latitude point on the globe (there are 64800 of them in total, and they were measured on 454 different time stamps, between 2002 and 2016).  This model includes intercept, velocity, acceleration, annual, half annual and
1/3 annual oscillation estimates, and can express any point at any time on the globe.  After this, a separate singular value decomposition and a principal component analysis was made for the data.  In this way, it was possible to either analyze the points individually, create a regional (mask) analysis of any place on the Earth, or analyze all of it globally.  Additionally, the accuracy of the data was determined using {P-}values, as well as a Root-Mean-Square error estimate.
In  the  global  analysis,  an  overview  of  the  water  distribution,  as  well  as  its  dynamical changes between 2002 and 2016, was made.  The regression model and the principal component analysis were made for the entire globe, which helped determine what areas were interesting to examine in detail, by looking at the magnitude of the signal, the rate of change, and the magnitude of the amplitude, as well as the phase of different regions.
Following the creation of the global analysis, 7 different regional areas on the globe were studied  in  closer  detail,  by  creating  a  mask  around  them.   These  different  regions  express information  about  different  phenomena,  such  as  ice  loss  trends  observed  in  the  Arctic  and Antarctic regions, annual oscillations in the rain forests, or large-scale earthquakes in Sumatra or Fukushima.  At the end of the paper, the final days of the {GRACE} satellites, as well as their successor  mission  the  {GRACE}  Follow-on  mission,  are  briefly  covered.   A  discussion  of  each regional area follows, to attempt to interpret the findings of the results and what implications they might have.
Per the results of the analyses, the areas that were gaining or losing mass in the Arctic and Antarctic regions of Greenland, Alaska, and Antarctica were identified (for example, ice-loss trends were decelerating in south-eastern Greenland, but accelerating in south-western Greenland),  and an estimate of the magnitude of annual ice loss was made and visualized for the period of 2002-2016 for these areas as well.  In northern South America,  the amplitude and phase of the annual oscillation were determined for different areas.  In the Caspian Sea located between Europe and Asia,  the decline and rate of decline of its water levels were estimated and plotted over time.  In the Tibetan Plateau and the Himalayan mountain range, the shift-of water-mass balance was determined as well as the magnitude of this shift, between the two regions.  Moreover, for Sumatra and Fukushima, the resulting spikes from the gravity change after the large-scale earthquakes of the 21st century were analyzed, resulting in a geographic visualization of the tectonic plate boundaries and movements in these two regions, as seen in the spatial pattern of the principal component analyses."
}