1. By what astrology of fear or hope

2. Dare I to cast thy horoscope!

3. By the new Moon thy life appears;

4. Longfellow, To a child

Tidal analysis of data collected by observations of sea levels and currents has two purposes. Firstly, a good analysis provides the basis for predicting tides at future times, a valuable aid for shipping and other operations. Secondly, the results of an analysis can be interpreted scientifically in terms of the hydrodynamics of the seas and their responses to tidal forcing. An analysis provides parameters that can be mapped to describe the tidal characteristics of a region. Preliminary tidal analyses can also be used to check tide gauge performance, as discussed in Chapter 2.

The process of analysis reduces many thousands of numbers, for example a year of hourly sea levels consists of 8760 values, to a few significant stable numbers that contain the soul or quintessence of the record [1]. An example of statistical tidal analysis is given in the description of sea levels in Section 1.6. In tidal analysis the aim is to produce significant time-stable parameters that describe the tidal régime at the place of observation. These parameters should be in a form suitable for prediction, should be related physically to the process of tide generation, and should have some regional stability.

The science of measurement

The ocean is its own uncontrollable laboratory and the oceanographer who measures the properties of the sea is an observational rather than an experimental scientist. Sea levels can be measured in situ, or by altimetry-satellite remote sensing. Technically the necessity of making in situ measurements of sea level presents many challenges in terms of the logistics of travel to the site, for deployment of the equipment, and for its safe and reliable operation in a frequently hostile environment.

This chapter summarises methods of measuring changes of sea levels over tidal and longer periods. The special requirements of tsunami monitoring are further discussed in Chapter 8. Measurements of currents are not included here (but see Section 4.4 on analyses of currents) as they are covered in many general oceanographic textbooks. Measurements of sea level by satellite altimetry, which are closely linked to orbit computations, mean sea level (MSL), and the shape of the Earth, are discussed extensively in Chapter 9.

1. . . . we cannot tell

2. When any given tide on the heart’s shore

3. Comes to the full.

4. . . . Few could endure

5. That knowledge, and not die.

6. It is better to be unsure.

7. Jan Struther, High Tide

The application of sea-level and tidal knowledge to the design and construction of useful marine structures and systems includes:

• harbour design and operation,

• design of coastal defences to resist flooding,

• coastal sediment control, groynes,

• flood warning systems,

• estuary, wetland, lagoon and inlet management,

• offshore structures for gas and oil extraction,

• schemes for generating power,

• cooling water intakes, effluent discharges to the sea,

• climate change forecasts and planning.

Tides offer many invaluable on-going environmental services that are not costed or charged. Ship routing between ports has used tides since historical times. Most of the great ports of the world are situated near the mouths of large rivers and many are a considerable distance inland. London, on the River Thames, and Hamburg, on the River Elbe, are good examples of inland ports. By travelling inward on a flooding tide and outward on an ebbing tide, ships can make considerable savings of fuel and time. The vigorous tidal currents serve to keep channels deep. The tidal flows can also prevent harbours freezing during winter, for example in New York, both by their mixing action and by the introduction of salt water which lowers the freezing point. Pollution, inevitably associated with large industrial developments and centres of population, is also more readily diluted and discharged to sea where there are regular exchanges of tidal water. The conditions for ports where tidal ranges are relatively large may be contrasted favourably with those, for example Marseilles, where tides are small. The pollution problems are much greater in the Mediterranean, and despite their high rates of fresh-water discharge, neither the Rhône nor the Nile have proved navigable for any but the smallest sea-going vessels.

When planning marine engineering works, the design parameters include not only sea-level changes: tides, surges, tsunamis and mean sea level (MSL), but also waves, winds, earthquakes, sediment movement, marine fouling and ice movement. Here we focus only on the sea-level aspects of the design engineer’s considerations.

1. And Noah he often said to his wife when he sat down to dine,

2. ‘I don’t care where the water goes if it doesn’t get into the wine.’

3. G. K. Chesterton, Wine and Water

Introduction

This chapter discusses a number of aspects of variability and long-term change in mean sea level (MSL). The changes take place on timescales of months through to centuries and can be studied with tide gauge, altimeter and some other data types, combined with different types of numerical modelling. The variations considered have amplitudes measured in centimetres or decimetres for most timescales and at most places. However, much larger variations do take place at some locations. For example, seasonal sea-level changes of around a metre are observed in certain parts of the Bay of Bengal in the Indian Ocean, and variations of several decimetres to a metre occur approximately every 3–7 years in the Pacific during El Niño events. A similarly large rise may occur throughout the world ocean during the next 100 years if some predictions of anthropogenic climate change prove correct.

The real world

The Equilibrium Tide developed from Newton’s theory of gravitation consists of two symmetrical tidal bulges, directly under and directly opposite the Moon or Sun. Semidiurnal tidal ranges would reach their maximum value of about 0.5 m at the equator. The individual high water bulges would track around the Earth, moving from east to west in steady progression. These characteristics are clearly not those of the observed tides.

The observed tides in the main oceans have mean ranges of about 0–1 m (amplitudes 0–0.5 m), but there are considerable variations. The times of tidal high water vary in a geographical pattern, for the daily solar and semidiurnal lunar tides, which bears no relationship to the simple ideas of a double bulge. The different tidal patterns generated by the global and local ocean responses to the tidal forcing are clear in Figure 5.1. The tides spread from the oceans onto the surrounding continental shelves, where much larger ranges are observed. In some shelf seas the spring tidal ranges may exceed 10 m: the Bay of Fundy, the Bristol Channel, the Baie de Mont Saint Michel and the Argentine Shelf are well-known examples of big tides. In the case of the northwest European shelf, tides approach from the Atlantic Ocean in a progression to the north and to the east, which is quite different from the Equilibrium hypothesis.

Introduction

Mean sea level (MSL) records contain many examples of relative sea level being affected by geology as much as by the oceanography and climate discussed in the previous chapter. Figure 11.1 shows three examples; many more can be found in the scientific literature [1]. Unlike the sea-level rise experienced during the twentieth century at most locations around the world, the MSL record at Stockholm in Sweden shows a sea-level fall of approximately 4 mm/yr, which is a consequence of the land on which the tide gauge is situated experiencing a high rate of crustal uplift due to Glacial Isostatic Adjustment (GIA) [2, 3]. The record from Nezugaseki shows an example of a near-instantaneous change of MSL of about 20 cm due to the 1964 Niigata earthquake off the west coast of Japan [4]. Both of these examples are due to natural processes in the solid Earth. The third example is of a change in land level (and so relative sea level) due to an anthropogenic process, in this case groundwater pumping under Bangkok, Thailand [5]. Any analyst of MSL records will be aware of such large signals. However, the possibility of other, smaller and more subtle, signals in the data set cannot be excluded, and anyone who uses the records primarily for ocean or climate research must always be aware of them.

1. Mere anarchy is loosed upon the world,

2. The blood-dimmed tide is loosed, and everywhere

3. The ceremony of innocence is drowned.

4. W. B.Yeats, The Second Coming

Introduction

In the past few years, two giant tsunamis caused by undersea earthquakes have caused major loss of life and damage to coastal infrastructure. On 26 December 2004, a moment magnitude (Mw) 9.3 megathrust earthquake, the third largest on record, took place along 1600 km of the subduction zone from Sumatra to the Andaman Islands in the eastern Indian Ocean [1, 2]. The resulting tsunami waves caused enormous damage, particularly in Indonesia, India, Sri Lanka and Thailand, and killed more than 230,000 people (Figure 8.1) [3, 4]. On 11 March 2011, the Tōhoku (or Sendai) Mw = 9.0 megathrust earthquake, the fourth largest on record, occurred 130 km off the east coast of Japan leaving some 20,000 people dead and tremendous destruction of coastal infrastructure (Figure 8.2), including a major nuclear emergency at the Fukushima Daiichi power plant [5]. These two catastrophic events have had many important consequences including, it will be seen, within sea-level research.

1. Prospero: ‘. . .ye that on the sands with printless foot

2. Do chase the ebbing Neptune and do fly him

3. When he comes back’

4. Shakespeare, The Tempest

Sea levels are always changing, for many reasons. Some changes are rapid while others take place very slowly. The changes can be local, or extend globally. This book is about the science of these changes.

In this first chapter we outline what constitutes sea-level science. A brief account of the development of scientific ideas is followed by an outline of how sea levels are affected by a wide range of physical forces and processes. Finally we give some basic definitions, and discuss the fundamental statistics of sea levels as time series.

Background

Living by the sea has many benefits. Statistics show that about half the global population lives within 100 km of the sea. Most of the world’s largest cities are on or near the ocean. Ninety per cent of all global trade is carried by sea. The coast offers possibilities of both trade and travel, and increasingly of water-based recreation. Natural geological processes have often conspired to create flat and fertile land near to the present sea level, to which people are drawn or driven to settle.

In Chapters 2 and 9 we looked at different tidal levels and their use as zero or Datum Levels [1]. Tidal datums are also used to define shorelines, adopted as the state, national and international boundaries shown on maps. Generally the important levels are some form of High Tide, or some form of Low Tide, depending on locally adopted definitions. The determination of these levels, and their projection to mapped shorelines may require long records of sea-level measurements, often a complete nodal cycle of 18.61 years. Inevitably, knowledge of tidal principles has an important role to play in the development and interpretation of legal rules, but the technical aspects of defining tidal boundaries have sometimes been underemphasised [2].

The three components of a robust boundary definition are:

• clear and measurable tidal level parameters,

• a means of converting these levels into map coordinates,

• a legal system for interpreting and enforcing the boundaries.

To these we might add a process for adjusting to tidal and coastal changes over the long-term.

Introduction

Geodesy is a branch of science that is concerned with the Earth’s time-dependent geometric shape, gravitational field and rotation. Over 70 per cent of our planet is covered by ocean, and its shape is largely defined by the mean sea surface, so geodesy and sea-level science are intimately connected. A number of classic texts on geodesy are available [1, 2], and also excellent reviews of modern geodetic techniques [3]. In this chapter, we confine ourselves to a description of some of the main developments in geodesy that relate to understanding the spatial variations in the sea surface. In the next chapter we discuss its temporal variations.

The International Terrestrial Reference Frame

A principal goal of geodesy is to assign coordinates to points on the Earth’s surface as a function of time. Such a time series could be, for example, the height of sea level at a particular location (latitude, longitude) in the ocean, or the height of a benchmark on land. It is important to know something of the geodetic framework within which many of the sea- and land-level measurements described later in this chapter are made.

Introduction

This chapter contains our personal selection of topics on how the tides and sea-level changes have played important roles in the development of life, and in human history. The populations of coastal zones are increasing dramatically, and tides, storm surges and long-term sea-level changes will continue to play important roles in our lives. Impacts of sea-level change will take place alongside those due to many other climate and environmental stresses.

It is our belief that, if these impacts are to be avoided, or managed, as far as possible, then we have to learn more about the space and time scales of sea-level change and the various reasons for them. Also we have to communicate a greater appreciation of how tides and sea levels have contributed to the coastal environment in general, providing many communities with food sources and places to live and thrive, contributions that continue in many and varied ways today.