An approach for estimating time-variable rates from geodetic time series

Abstract

There has been considerable research in the literature focused on computing and forecasting sea-level changes in terms of constant trends or rates. The Antarctic ice sheet is one of the main contributors to sea-level change with highly uncertain rates of glacial thinning and accumulation. Geodetic observing systems such as the Gravity Recovery and Climate Experiment (GRACE) and the Global Positioning System (GPS) are routinely used to estimate these trends. In an effort to improve the accuracy and reliability of these trends, this study investigates a technique that allows the estimated rates, along with co-estimated seasonal components, to vary in time. For this, state space models are defined and then solved by a Kalman filter (KF). The reliable estimation of noise parameters is one of the main problems encountered when using a KF approach, which is solved by numerically optimizing likelihood. Since the optimization problem is non-convex, it is challenging to find an optimal solution. To address this issue, we limited the parameter search space using classical least-squares adjustment (LSA). In this context, we also tested the usage of inequality constraints by directly verifying whether they are supported by the data. The suggested technique for time-series analysis is expanded Institute for Geodesy and Geoinformation, University of Bonn, Nussallee 17, 53115 Bonn, Germany to classify and handle time-correlated observational noise within the state space framework. The performance of the method is demonstrated using GRACE and GPS data at the CAS1 station located in East Antarctica and compared to commonly used LSA. The results suggest that the outlined technique allows for more reliable trend estimates, as well as for more physically valuable interpretations, while validating independent observing systems.

Detecting time-varying seasonal signal in GPS position time series with different noise levels

“…The addition of temporal correlated noise in the state vector was found to give superior results compared to the KF of Davis et al (2012) who did not include this type of noise. We concur with Didova et al (2016) that the search for the optimal values of the variances of the temporal correlated noise and the random walk part of the seasonal signal is a complex problem. However, when this task is well done, the KF is able to estimate better the varying seasonal signal at normal to high noise levels than the afore-mentioned methods.…”

“…Then, we implemented both filters, but after tuning the filter of Davis et al (2012), we could not obtain misfits lower than 0.21 and 1.15 mm for the 1 and 10 mm/ year 0.25 noise levels, respectively. These values are larger than the values we obtained using the filter of Didova et al (2016). Therefore, the latter was used in this research.…”

“…The KF, with a correct tuning of the variances in the filter, as described by Didova et al (2016), was found to be the most precise method for estimating the varying seasonal signal. The addition of temporal correlated noise in the state vector was found to give superior results compared to the KF of Davis et al (2012) who did not include this type of noise.…”

“…As a result, the power spectrum of the noise in the GPS position time series flattens for frequencies below the annual period. However, as it was shown by Didova et al (2016), it can be modified by adding the ε(t) term in the form of a third-order autoregressive model which mimics a power-law noise. They tuned their filter so that the low frequencies were not absorbed in the stochastic part.…”

“…As explained in the previous section, the KF method of Davis et al (2012) differs from the one of Didova et al (2016), as, in the former, the temporal correlated noise was omitted in the state vector. To obtain the best fit, we tried various values for the variances by which the amplitude of the seasonal signal is assumed to vary between each of the time steps.…”