Jean-Philippe Montillet - Geodetic Time Series Analysis in Earth Sciences

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Students of high school physics often encounter a fictional flat Earth where objects move without friction through a vacuum. As they grow in their understanding, the complexities of sphericity and friction emerge; but gross simplifications often remain of the real system being modelled. This is the world of the so-calledand humorousspherical cowa visual metaphor for highly simplified models of complex phenomena.

Students of geodesy will have been (or should have been) taught the complementarity of functional and stochastic models of a processfor any given problem, any signal (including noise) must be considered appropriately in the functional model or the stochastic model. Neglect of any component of the signal produces erroneous and potentially misleading estimates of parameter values and their uncertainties.

In the past, it was common in geodetic analysis to assume (usually untested) that the functional model was complete, and the residual noise was white (temporally uncorrelated) and could be treated as such in the stochastic model. A more robust analysis of various geodetic signals has found that such time series normally contain time-varying signal and noise is rarely white.

Because of these previous assumptions, there is little doubt that scientific conclusions have been reached that are not actually supported by the data: statistically insignificant accelerations in ice sheets have been interpreted as significant; noise has been interpreted as genuine strain in Earths crust; changes in linear rates of sea level rise have been too confidently declared; seasonally varying deformation of the solid Earth was approximated as time-constant annual harmonic. These (not-entirely) hypothetical examples have major implications that extend well beyond geodesy and geophysics and into society and policy. Spherical cows are not sufficient.

In my own research field which focuses on geodesy in polar regions, the developments summarised in this book have advanced our understanding tremendously. New insights have been gained into the three-dimensional deformation of Antarctica due to tectonics and surface loading changes over months to millennia, while more robust estimates of ice mass change and their uncertainties have been obtained from the Gravity Recovery and Climate Experiment (GRACE). And yet much analysis remains overly simpleit is still common to adopt simple models of linear or quadratic changes in ice mass or volumeand the residuals are often treated as white noise or simple autoregressive processes both of which are typically not realistic. There is still much to do although the growing body of excellent software tools means that major advances in rigour are within reach.

The focus of this book is to synthesise recent progress in geodetic time series analysis theory and approaches that represents a shift away from a spherical cow to a not-so-spherical cow. This book is both theoretical and practical. It shines a light on a new theory, explores different methodologies and, helpfully, showcases the implementation of methodology into practical tools to assist the entire community in undertaking more robust time series analysis.