Transferring a Survey Datum Across Water

Introduction

Transferring a survey datum across water to an island or offshore beacon using traditional survey methods is difficult, expensive, and not very accurate. But there is another way that is not so expensive and is usually more accurate. It involves fairly sophisticated modern data analysis tools. It also requires a tide gauge on the mainland that is levelled in to the desired datum, and another tide gauge at the offshore location.


Here is an application in Otago, New Zealand, where we wanted to establish the datum on Green Island to be the same as Chart Datum at the Port tide gauge in Otago Harbour. There is an open coast sea-level recorder on the island that has 3 years of data available.



The Concept

The concept is that long-term (> 1 month) fluctuations in sea level are uniform over a large area of ocean; therefore, they can be used to transfer levels between tide gauges.

MLOS

Long-term fluctuations in sea level arise from the following factors:

We call these fluctuations “mean level of the sea” (MLOS) to distinguish them from mean sea level (MSL) which is often used as a term meaning a fixed survey datum. MSL is usually the MLOS for a particular year. For example, in Christchurch city, MSL datum is the MLOS for 1931 at Lyttelton, so allowing for the average sea-level rise of 1.7 mm/y for 75 years, MSL is more than 0.1 m below present day MLOS.

Calculating MLOS

MLOS is calculated from hourly tide gauge data using the following steps:

  1. Forecast the tide and subtract it from the record – this forms the “residual”.
  2. Low-pass filter the residual to remove long waves, residual tide, and storm surge.
  3. Decimate the low-pass filtered residual by taking monthly means.


The most important of these steps is low-pass filtering. The preferred method is orthogonal wavelet decomposition because it accommodates the non-stationary nature of the signal, where most other algorithms assume the signal is stationary in other words, its variance, or energy, is not affected by the length of the window used to sample it.

Removing the tide first is desirable, though not essential. The tide usually represents more than 90% of the energy in the signal, varying by ±1 m or more twice daily, whereas we are looking for fluctuations of ±0.01 m every month. So, subtracting the tide removes the risk of it contaminating the low-frequency part of the signal.

Decimate is an interesting word. It comes from the Roman legions where the penalty for cowardice or mutiny was for every tenth man (drawn by lot) to be executed by his colleagues. Nowadays, in signal processing we use it to describe the concept of downsizing a record, thereby increasing the interval between samples.

Using MLOS to Calculate the Datum

Once we have MLOS at both sites, we can compare them and calculate the difference in datums between the sites. We do this simply by calculating the mean difference and using a Student's t test to estimate the confidence intervals. For Green Island, the mean difference in datum from Port Chalmers Chart Datum was 1.313 m with a 95% confidence interval of ±0.007 m. MLOS at Port Chalmers is compared with MLOS at Green Island less 1.313 m in the plot below. Note that once the datum is applied, individual differences in MLOS as large as ±0.055 m occur; however, the Student's t test tells us that the mean difference is accurate within ±0.007 m at the 95% level.

An interesting side issue arose while working on the above example. When we used data from the Spit, instead of Port, for assessing the datum, this is what the comparison of MLOS looked like, where the plot shows the difference between MLOS at the two sites:


Notice that for the first part of the record (up until mid-2005), the points oscillate about zero, then they drop in a consistent manner. This implies that relative to Green Island, the Spit record is drifting upwards. Further investigation revealed that this was in fact the case: the pile the recorder was mounted on was sinking, thus causing the depths to appear to be getting larger. Surveyors checked the amount the pile had dropped and found it was 6 cm, which agrees remarkably well with what the MLOS tells us.

Finally, we can use MLOS to establish the accuracy of the traditional land surveying that has been done to transfer the Port datum to the other tide gauges in the harbour, as shown in the Table below, where for the Spit we used only the data prior to mid-2005 when it started to drift. The table shows that if we use Port as the datum, then the datum at the Spit is 0.022 m lower than it should be and the datum at T-Shed is 0.028 m lower than it should be.


Comparison of datums with 95% confidence intervals
Station  Mean m  95% CI m 
Port vs Spit  0.022  ±0.003 
Port vs T-Shed  0.028  ±0.003 
T-Shed vs Spit  -0.006  ±0.005 


Summary

For transferring a datum across water to an island or offshore beacon that has a tide gauge, an accurate and relatively inexpensive method is to use the information on the long-term fluctuations in sea level, namely MLOS, that are in the tide gauge records.


Please address enquiries to:
Derek Goring
Mulgor Consulting Ltd
Christchurch
New Zealand