Stochastic Modelling of Geophysical Signal Constituents Within a Kalman Filter Framework

Abstract

Reliable trend estimation is of great importance while analyzing data. This importance is even enhanced when using the estimated trends for forecasting reasons in the context of climate change. While a constant trend might be a valid assumption for describing some geophysical processes, such as the tectonic motion or the evolution of Glacial Isostatic Adjustment (GIA) over very short geologic time frames, it is often too strong of an assumption to describe climatological data that might contain large inter-annual, multi-year variations or even large episodic events. It is therefore suggested to consider signal as a stochastic process. The main objective of the work described in this chapter is to provide a detailed mathematical description of geodetic time series analysis which allows for physically natural variations of the various signal constituents in time. For this purpose, state-space models are defined and solved through the use of a Kalman Filter (KF). Special attention is paid towards carefully estimating the noise parameters, which is an essential step in the KF. It is demonstrated how the time-correlated observational noise can be classified and handled within the state-space framework. The suggested methodology is applied to the analysis of real Gravity Recovery And Climate Experiment (GRACE), Global Positioning System (GPS), Surface Mass Balance (SMB) and global mean sea level time series. The latter is derived based on different satellite altimetry missions. The examples are illustrative in showing how the outlined technique can be used for estimating time-variable rates from different geodetic time-series with different stochastic properties.