Estimating decadal variability in sea level from tide gauge records: An application to the North Sea

One of the primary observational data sets of sea level is represented by the tide gauge record. We propose a new method to estimate variability on decadal time scales from tide gauge data by using a state space formulation, which couples the direct observations to a predefined state space model by using a Kalman filter. The model consists of a time-varying trend and seasonal cycle, and variability induced by several physical processes, such as wind, atmospheric pressure changes and teleconnection patterns. This model has two advantages over the classical least-squares method that uses regression to explain variations due to known processes: a seasonal cycle with time-varying phase and amplitude can be estimated, and the trend is allowed to vary over time. This time-varying trend consists of a secular trend and low-frequency variability that is not explained by any other term in the model. As a test case, we have used tide gauge data from stations around the North Sea over the period 1980-2013. We compare a model that only estimates a trend with two models that also remove intra-annual variability: one by means of time series of wind stress and sea level pressure, and one by using a two-dimensional hydrodynamic model. The last two models explain a large part of the variability, which significantly improves the accuracy of the estimated time-varying trend. The best results are obtained with the hydrodynamic model. We find a consistent low-frequency sea level signal in the North Sea, which can be linked to a steric signal over the northeastern part of the Atlantic.