Refining linear trend estimates from one dimensional time series data with autoregressive covariance modelling: an application to GRACE total water storage time series data

Abstract Deriving trend functions from observed time series is one of the main tasks in the field of signal processing. Separating the observation into a deterministic function, a stochastic residual signal and a stochastic noise component using dedicated model representations enables further study of these individual components, e.g. screening for climate signals. Whereas the deterministic part is modelled as a linear combination of basis functions, the use of autoregressive processes to model the noise and signal is proposed. Within an iterative estimation scheme, the uncertainty information of the observed variables is properly modelled and carefully propagated to the resulting parameters. This enables the use of statistical testing and Least-Squares Collocation in further investigations of the separated signal components. In this study, the proposed iterative procedure is applied to relatively short total water storage time series derived from measurements of the satellite mission GRACE. The trend in total water storage is, for instance, relevant for climate studies, identifying regions getting drier or wetter. Accounting for the aforementioned covariance information based on autoregressive processes allows the use of Hypothesis tests to identify regions with significant trends. On the contrary, the smoothed stochastic signal components are required to identify extreme/anomalous events like floods and droughts in the observed time series. Additionally, to improve the estimation of the stochastic signal, data from numerical models are used to estimate the process characteristics.