Tides in a changing climate

The largest contribution to sea level variability in many parts of the world is the tide. In addition to sea level rise, the tides are changing in many parts of the world (Woodworth, 2010). The aim of this project is to develop methods to analyse and predict tides under changing conditions, to improve projections of flooding events in future climate scenarios. The project would particularly suit a mathematically able candidate.

Tides are caused by the gravitational action of the sun and moon, which are extremely predictable. However, the tidal response to forcing changes as the medium in which the tide is generated changes. That means climate-related (and other) changes to the ocean, rivers, and shape of the coastal region, can produce changes in the tide at a wide range of time scales.
This causes complications, as traditional tidal analysis is based on the assumption that the tidal response to the moon and sun is “stationary”, i.e. independent of time. The aim of this project is to develop new methods of tidal analysis that are applicable to non-stationary tides, making it possible to identify the physical mechanisms that cause changing tides, and to project those changes into the future.

Examples of changes which can influence the tides are changes in river flow (Hoitink and Jay, 2016), and weather-driven storm surge events (Williams et al., 2016; 2018). In order to incorporate such changing conditions into tidal analysis, we need to be able to simultaneously fit the tides and the relevant changing parameter to the observations. Various methods have been attempted to tackle this, e.g. those described in Hoitink and Jay (2016) and Hibbert et al. (2015), but they tend to be hampered by being based on a traditional description of the tide with a large number of astronomical parameters.
The aim here will be to use ideas from dynamical systems theory (nonlinear oscillators) to develop a new method of performing tidal analysis which is not tied to ideas of stationarity. This is based on the observation that tidal models do not have a long “memory”, meaning the tide is only sensitive to forcing over the past few months. The method is founded on a reduced phase space embedding as described in Broomhead and King (1985). Once developed it has the potential for very widespread use.

The initial stages will involve developing the simplest form of the method, without time dependent parameters, and comparing it to traditional tidal analysis. For this, a wide range of resources at the NOC, Liverpool will be brought to bear, including datasets, model outputs, and tidal analysis software. Once the basic method has been established, research will enter a more exploratory mode to determine how time varying parameters can best be identified. The method will then be used to analyse and interpret tides in difficult conditions, and to assess the likely change of tides which will result from future changes in, e.g. river flow or modes of climate variability such as ENSO (El Niño – Southern Oscillation).