Models for Correcting Hydrographic Surveys

For hydrographic surveys in which corrections need to be made for sea-level conditions, computer models can provide the information accurately and at low cost.

Introduction

Sea level consists of a whole spectrum of oscillations at different timescales. These result from a wide range of physical forcing functions. Usually, these days, hydrographic survey systems have heave compensation that accommodates sea and swell waves, but all of the remaining phenomena in the spectrum contribute to errors in the survey to a greater or lessor extent. Some of them, such as rissaga and tsunami, are transitory, but others, such as infra gravity and far infra gravity waves can be ubiquitous. This results in topography that looks like a corrugated iron roof, unless they are properly allowed for. But usually the most important phenomena are the combined effect of tides, storm surge and mean level of the sea (MLOS) and these are accurately captured by a tide gauge or a set of tide gauges. In many places, the tide varies very little spatially and one or two tide gauges are sufficient. However, there are some circumstances where the spatial variability of the tide is so great that a single tide gauge is inadequate, and deployment of an array of temporary tide gauges is either impractical or too expensive.

Sea Level Spectrum

Phenomenon  Timescale  Forcing 
Sea  < 7 s  Local Wind 
Swell  7 to 20 s  Large-scale wind events 
Infra Gravity  20 to 120 s  Swell waves breaking on adjacent beaches 
Far Infra Gravity  2 to 30 min  Grouping of swell waves 
Rissaga  5 to 40 min  Rapidly-moving low-pressure systems 
Tsunami  5 to 60 min  Earthquakes, submarine avalanches, volcanoes 
Tides  4 to 24 h  Gravitational attraction of Moon and Sun 
Storm Surge  1.5 to 15 days  Changing atmospheric pressure and wind 
MLOS  > 15 days  Climatic effects 

Highly Variable Tide

There are many places around the world where the spatial variability of the tides makes accurate hydrographic survey difficult. For example, The Arabian Gulf, the Red Sea, and Antarctica, but one place where the problem is particularly profound is Cook Strait between the North and South Islands of New Zealand.

The figure to the left is called a "cotidal chart" in which the amplitude of the tide (in this case the semidiurnal lunar, M2, tide) is shown as filled contours and the phase is shown as lines.
The area shown is Cook Strait, where the amplitude of M2 goes to almost zero on the southwest coast of the North Island. This is called an amphidrome. From this point, the phase lines radiate like spokes of a wheel and the time of high tide varies rapidly from place to place. Furthermore, as we move away from the amphidrome, the gradient in amplitude is very large, varying by up to 0.6 m in 30 km.
How many temporary tide gauges would be needed to accurately encapsulate this information?

TideModels

A solution to the problem is to use a tide model in which the individual tidal constituents are determined on a grid. Then, to obtain the tide at a particular time and place, the constituents are interpolated and a tide forecast is done.
There are two sorts of tide model available:

Global Tide Models

There are many global tide models available. Most of them are derived from data from the oceanographic satellite TOPEX/Poseidon.

They provide up to 13 of the main tidal constituents, on a rectangular grid with spacing of between 0.25 and 1º of latitude and longitude.

The models use ground-truthing from tide gauges and hydrodynamic considerations, and this governs how accurate they are close to the coast.

For remote locations such as around New Zealand, the global models are not accurate near the coast.
For Antarctica, they give quite erroneous results, mainly because TOPEX/Poseidon does not cover the region below 65ºS.

Local-Area Tide Models

There are two types of local-area tide model:

Hydrodynamic Model

Hydrodynamic models solve the shallow water equations using the tidal constituents from a global model for the deep-water boundary conditions. They also take account of ocean-loading tides (deflection of the Earth’s crust in response to the tide) and Earth tides (deflection of the Earth’s crust in response to the direct gravitational attraction of Sun and Moon). The accuracy of a local-area tide model depends upon the accuracy of the local bathymetry and shoreline. Usually, these can be defined in much finer detail in a local-area model than in a global tide model, and hence the accuracy is much enhanced. Of course, if we already had accurate bathymetry and shoreline alignment, hydrographic survey would not be required, so it is a “dual problem”: to get an accurate hydrodynamic model, you need accurate bathymetry; but to get accurate bathymetry, you need an accurate tide model.

Finite element grid for tide model of NZ's EEZ

Surface-Fitting Model

Surface fitting models simply use measured data to provide a set of points through which a smooth surface is fitted. These models require a dense network of tide gauges to get accurate results, whereas hydrodynamic models do not rely on tide gauges, except for model validation.

Tide stations in Arabian Gulf with amplitudes in cm of the K1 tide

Each method has its advantages and disadvantages. In situations where there are amphidromes and their position is important, surface-fitting may be preferred because in positioning amphidromes, hydrodynamic models are very sensitive to local bathymetry and shorelines, as well as fluctuations in the ocean-loading tide. However, there are few places where the tide-gauge network is dense enough to provide the data needed to obtain an accurate surface-fitting model, though the Saudi coast of the Arabian Gulf may be an exception.

Storm Surge Model

Storm surge is the response of the ocean to changing atmospheric pressure and wind. It has timescales of 1.5 to 15 days, and usually its spatial variability is much less than tides. Of course, in storms this may not be true, but surveys are not normally carried out in storms.
During the hydrographic survey of Foveaux Strait, at the south of the South Island of New Zealand (see below), there was concern about the possible east-west variability of storm surge across the strait. This area is exposed to the vast Southern Ocean and experiences significant storm surge events every two weeks on average.
To address this concern, a tide gauge was deployed at Puysegur Point on the western side and its storm surge was compared with the storm surge measured at the permanent site on Dog Island on the eastern side. The distance between the gauges was 150 km.
The results were surprising. Except for storms (when no one in their right mind would be trying to survey in Foveaux Strait), there was no significant difference in storm surge between the two sites.
Subsequently, the storm surge from Dog Island was used for the entire survey area.



Mean Level of the Sea (MLOS)

MLOS varies from month to month in response to:

MLOS should not be confused with mean sea level (MSL), which is a fixed datum. Usually, MSL is the MLOS averaged over a particular year. The importance of MLOS to hydrographic surveying is that if a temporary tide gauge is used, it needs to be correlated with the nearest long-term tide gauge, otherwise there will be an offset corresponding to the current MLOS. The size of this offset can be several cm, as illustrated in the figure below.

Typical variation of MLOS (mean level of the sea) over a two year period. At this site, MSL is based on the average MLOS for 1998. The average MLOS over the period shown was 0.046 m above MSL.

Summary

A wide range of models are available for correcting hydrographic surveys for sea-level variability. Each survey needs to be assessed for the variability of tides across the domain and to determine whether a few temporary tide gauges will suffice. If more than a few gauges are required, a tide model of one sort or another is probably the most economic option. However, the tide model needs to be supplemented with storm surge and MLOS models. Often these can be simply extracted from the nearest permanent tide gauge. Whether or not a tide model is used, the survey needs to be corrected for MLOS from the nearest permanent tide gauge.

For more information contact:
Derek Goring
Mulgor Consulting Ltd
Christchurch, New Zealand.