# High resolution global modelling of ocean tides

Lead Research Organisation: University of Leeds
Department Name: Applied Mathematics

### Abstract

Tides are usually thought of as regular variations in the height of the sea surface. What we think of as `the' tide is made up of many distinct tidal signals - some driven by the Sun and some by the Moon - the largest of which oscillate up and down over about 12 or 24 hours. These tides operate more or less independently, and sometimes reinforce each other to give an unusually large tidal range (spring tides) and sometimes partially cancel each other to give an unusually small tidal range (neap tides). At most coastal locations the 12 hour family of tides give the dominant response (such as around the U.K.), but the 24 hour family of tides is larger in some locations (such as in the Pacific). The main aim of this project is to produce a computer model of ocean tides over the whole globe - but without using any data about the tides themselves. Such a model will simply use information about the forcing from the Sun and Moon, and the depth and shape of the oceans. This is an important goal, since until we can produce such a model we cannot be sure that we understand all the processes which shape the tides. A major obstacle to such models is the importance of a so-called internal tide. This is a distinct tide which occurs inside the ocean, and is barely visible from the ocean surface. It occurs because the ocean has cold (heavy) water at the bottom and warm (light) water at the top, allowing waves to be generated in between. The internal tides go hand-in-hand with the familiar tides at the surface, and indeed play an important role in determining them. So, to determine the tides at the surface we must also include the internal tides in our computer model. However, the internal tides have a short horizontal wavelength, ranging from about 5km to 150km, and significant computing resources are required to model these waves over the entire globe. The newest computer models attempt to do this, but in a rather inefficient way, requiring long simulations on large computers (and typically making some other approximations, too). We will construct our computer model in a completely different way, which promises to be much faster than other models, and will include the all-important details of the internal tides. The first output of this approach will be a model which will run on a desktop computer, producing global predictions of the eight main tidal signals in a few hours. However, we will extend this approach to look at finer details by developing an alternative version to run on a supercomputer. This will require the development of new algorithms to deal with the huge number of unknowns. The output of this model will be used to help us understand how tidal energy is transferred within the ocean. One of the main benefits of such computer models is that they can be used to predict tides in the past (or future). All that is required is a record (or prediction) of how sea level changes over time. There are reliable records of how the sea level has changed since the height of the last Ice Age, about 26,000 years ago, when sea levels were about 120 metres lower than at present. We will use these records to make a detailed examination of how tides have changed over this period of time. The details of these changes are interesting to oceanographers (who study the way in which energy is transferred around the ocean, and how this helps determine the global climate), and climate scientists (since it is possible that large Ice Age tides destructively interacted with floating ice shelves leading to rapid climate change).

### ORCID iD

Stephen Griffiths (Principal Investigator)  http://orcid.org/0000-0002-4654-2636

### Publications

10 25 50

Description Computer models of the ocean are often based on a rectangular grid with the coastline approximated as a series of steps. These stepped coastlines lead to small errors in models, which have been shown to be particularly worrying for computer models of tides: since large tides are often associated with a near-resonance of a coastal wave, it is crucial that the coastal wave dynamics are resolved to high accuracy. Alternative coastal approximations without steps have been developed to give more accurate tidal models.
Exploitation Route The new tidal model can be used to probe possible changes to tides in the future, driven by changes in sea level.
Sectors Aerospace, Defence and Marine,Energy,Environment

Title STM1C
Description A fully coupled barotropic/baroclinic global tidal model (i.e., surface tides and internal tides).
Type Of Material Computer model/algorithm
Provided To Others? No
Impact Ongoing; produces state-of-the-art global tidal simulations.

Description Invited research seminar at Imperial College London
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact This was a research seminar on tidal modelling, describing some of the new techniques (numerical and methodological) developed during the research project. There were some useful discussions about numerical modelling techniques with academics from related fields.
Year(s) Of Engagement Activity 2018