TECHNICAL ARTICLES

Measuring Water Level Corrections (WLC) Using RTK GPS

Brad Scarfe
University of Waikato, New Zealand

Abstract

Depths soundings need to be related to a survey datum by correcting for the water level at the time of the sounding. Traditionally this has been done by simultaneously, but separately, measuring tidal and heave corrections during a hydrographic survey. This practice is flawed because the effects of tides and heave are not separate, and are combined into the water level at any one instant. Measuring both corrections separately and then combining at the time of post-processing can introduce additional uncertainties. Measuring a Water Level Correction (WLC) using RTK GPS is considered a better methodology. Here,  measurement of a WLC, as well as separate tidal and heave corrections, is tested using a Trimble MS750 receiver.

Some solid-state heave devices require a survey vessel to travel at a constant speed and direction before each run line in order to stabilise. RTK GPS does not need to stabilise thus  making it a better alternative for short runlines and small survey areas such as ports, marinas and estuaries. The most important consideration is to precisely match GPS heights with soundings. A method for aligning the data within 10 milliseconds was  developed and is presented here. It is demonstrated that with  such a precise latency heave caused by long period swell (>5 second period), as well as short period waves (2-5 second  period), can be successfully corrected.

1.0       BACKGROUND

Hydrographic surveying is used to measure the topographic features of the seafloor in order to produce maps similar to those made of land areas with GPS and conventional survey techniques (Ingham and Abbott, 1992). It is a more complex task than undertaking a land survey because the height of the sea floor must be remotely measured with an echo sounder. Depth measurements, also referred to as soundings, need to be related to a suitable reference height. The reference height represents a datum such as lowest astronomical tide or mean sea level in calm water conditions (Kielland and Hagglund, 1995). Tides and waves constantly change the level of the sea making accurate measurement of the sea floor height even more difficult.

The two main sources of error in the surveying are poor spatial spread of soundings and error in measurement of soundings (Kielland and Hagglund, 1995). The first error source occurs because surveys attempt to represent a continuous sea floor with discrete points. Multibeam survey systems (Hughes Clarke et al, 1996 and Eeg, 1999) can represent a continuous seafloor more completely with a swath of soundings, but cost limits the application of this technology. The second error source is mostly due to poor sounder calibration and inaccuracies in measurement of corrections for tides and waves (heave). Real-time kinematic (RTK) GPS receivers can be used to minimise this second error source.

Traditionally the measurement of tidal and heave corrections have been done independently. This practice is imprecise because the effects of tides and heave are not separate, and are combined in the water level at any one instant. Measuring both corrections separately and then combining at the time of post-processing can introduce additional uncertainties and is more complicated than measuring a single Water Level Correction (WLC). High update, low-latency 3D RTK GPS measurement of a WLC is an accurate and convenient technique by which to reduce depth soundings to a datum. Although use of a WLC is promoted here as the best method, measuring the effect of tides and waves separately is more compatible with existing hydrographic software. It is therefore necessary to consider how to implement WLCs as well as RTK GPS tidal and heave corrections because, in the short term, it is more likely that people will adopt the latter approach.

The use of RTK GPS for measuring tidal and heave corrections has met resistance because of the limited capabilities of early receivers. Slow update rates, typically once per second (1Hz), and long data latency made the measurement of short period heave difficult. Modern, low latency (Betaille and Peyrey, 1999), high update rate (5, 10, 20Hz) receivers such as the Trimble MS750 can satisfactorily measure a WLC for many applications. The synchronisation of echo soundings and GPS positions can be calibrated easily and accurately making for a high precision of a WLC measurement, relative to other error sources in hydrographic surveying.

This paper summarises previous research on the use of RTK   GPS for tidal and heave corrections. New testing of the equipment confirms that the technology has reached the level of maturity  where it can be used for hydrographic surveying. The term WLC is discussed and its application to hydrographic surveying is detailed. The use of WLCs is identified as the preferred method for reducing soundings to a datum when the survey vessel is affected by tidal fluctuations and waves.

The Earth Science Department of the University of Waikato, New Zealand has been using a Trimble MS750 RTK GPS to measure WLCs as well as tide and heave corrections since late 2000. Their experiences have confirmed that RTK GPS can be used to measure a WLC for hydrographic surveys. There are various potential areas of improvement to software and hardware that have been identified through their experiences. These are discussed to help guide future development of the surveying technique.

2.0       Tidal and Heave Corrections

The measurement of tidal and heave corrections can be done using a variety of techniques. A common method for measuring a tidal correction is a pressure sensor-type tide gauge. Permanent tide gauges are often found in developed coastal areas, but may need to be deployed for the sole purpose of a survey if no other record is available. Using predicted tidal elevations is not accurate enough because of the influence of atmospheric pressure, wind stress, thermosteric effects (rain and temperature) and tidal shoaling. When there is a significant sea level gradient, as in some estuaries, two or more tidal records may be required from which tidal corrections can be interpolated.

Correcting for waves is more complex than tidal corrections. Heave in this context refers to the vertical movement of the survey vessel due to wave motion. The most basic form of heave compensation is to visually inspect sounding records and remove regular oscillations that were likely to be caused by heave (Kielland and Hagglund, 1995). The more commonly used method is to use a damped pendulum gyro or solid state device to measure vertical accelerations of the boat that can be integrated to yield a vertical distance travelled. The drawback with accelerometer type heave compensators is that a centrifugal effect is created when a vessel turns thus generating errors in the heave measurements. Some sensors require a survey vessel to navigate in a straight line for 30-60 seconds to allow the accelerometers to settle. This delay is not ideal for some surveying applications such as when short runlines only are being used (i.e. small areas that require a lot of turning). Accelerometers cannot measure long period waves (30-600 seconds) that occur as infragravity waves - dynamic wave set-up and wave set-down in the vicinity of the surf zone. These long period elevations and depressions can only be corrected by measuring a WLC.

2.1       Measurement of RTK GPS Tidal Corrections

Measuring tidal corrections using GPS can reduce the error caused by measuring tides from a remote location. This approach has the advantage of calculating tidal corrections in the same place as the sounding to which the correction is applied. The method involves averaging water level measurements over a period of time to give a tidal correction. Kielland and Hagglund (1995) investigated techniques for implementing measurement of tides with RTK GPS using a post-processing method. DeLoach (1995) and Ashkenazi et al. (1990) have also investigated the use of GPS for tidal measurement but in the context of long-term tide gauges.

2.2       Measurement of RTK GPS Heave Corrections

Two limitations of early RTK GPS systems for measurement of heave compensation were update rate and latency of observations. High-update, low-latency receivers have overcome these problems. Latency (Figure 1) refers to the time difference from when an observed position is measured and when it is displayed or stored on a computer or other data logger (Trimble, 1999).

Fig. 1: Factors contributing to latency of RTK GPS positions (Trimble, 1999).

For measurement of water level or heave corrections, the latency time must be both negligible and known so that it can be corrected. Commonly, the RTK roving receiver waits until reference receiver information is received. This method is called synchronised mode (Trimble Navigation, 1999). Typical accuracies for synchronised mode are ±2-3cm in the horizontal direction and ±3cm in the vertical and the transmission time between the two receivers produces a latency of ~2s. In order to achieve high update rates and lower latency, the rover accurately predicts the reference receiver carrier phase measurements a few seconds in advance, reducing the latency of observations. This is possible because the roving station can predict the path of the satellites, and atmospheric errors are constant over a small time scale. A slight degradation in accuracy is found with low-latency methods and typical accuracies for low latency mode are ±3cm in the horizontal direction and ±3-5cm in the vertical (Trimble Navigation, 1999).

2.3       Measurement of RTK GPS WLCs

Equations 1 and 2 show how a sounding is converted to a reduced level of the seabed (RL_SEABED ) by applying a WLC.

      RL_SEABED = WLC - D_ES                                                                        Equation 1

where               RL_SEABED        = Reduced level of seabed

                            WLC    = Water level correction

                            D_ES                          = Depth sounding

      WLC = H_GPS – H_A + D_TR + DS                                                                                                         Equation 2

where               H_GPS        = GPS antenna height relative to WGS84                                                                    ellipsoid

                            H_A         = Height of GPS antenna above water level

                            D_TR                          = Depth of echo sounder transducer below                                                               water level

                            DS        = Datum Separation

Theoretically, RL_SEABED remains constant when a boat floats over a stationary position in waves (Figure 2). This means that when a vessel rises because it is on the crest of wave, so must the value of WLC, hence D_ESincreases to keep the equation balanced. The converse is true when in the trough of a wave.

Fig. 2: Parameters for calculating seabed height before and during the passing of a wave.

A disadvantage of using RTK to measure water levels is that the GPS positions are calculated in terms of the WGS84 ellipsoid rather than a local datum. Thus the separation between the WGS84  ellipsoid and local geoid must be known. The WGS84 ellipsoid is a regular shaped, theoretical representation of the earth’s surface  while the geoid more correctly describes the earth irregularities in shape. The datum separation is very localised and varies greatly over  a small area, thus the use of a constant datum separation can be inadequate. The slope of the separation in Dunedin, New Zealand was found to be up to 77mm.km^‑1 (Kirk, 2000). When the datum separation is irregular, a small survey area (~25km²) can be calibrated by developing an inclined plane model. In some circumstances a constant datum separation can be used. For example, some survey jobs such as monitoring sediment infilling in a dredged channel or measuring beach profiles only require relative changes, so highly accurate datum separations are not needed.

3.0       Results of Previous RTK-GPS Trials

Various people have investigated the use of RTK GPS for hydrographic surveying. Prior research on the measurement of tidal and heave corrections is reviewed here.

3.1       Tidal Corrections

Figure 3 shows both empirically derived tides recorded over a two-hour period using the MS750 and those from a standard tide gauge (Baker, 1999). The RTK GPS positions were averaged every 60s using Trimble HYDROpro Navigation software (www.trimble.com/marine). The average difference between the two methods was 0.03m. It is important to realise that tide gauges have an accuracy specification of 0.01-0.03m and that errors will be present in both the GPS and the tide gauge record. The measured difference is within the expected accuracy of the system. The averaging period of 60s is considered too short to remove the effects of long period waves, seiches and errors in the measurement of GPS positions.

Figure 3. Comparison of RTK and tide gauge record (Baker, 1999).

3.2       Heave Corrections

Previous research into heave compensation by Kielland and Hagglund (1995) included the development of an algorithm to calculate heave corrections. A moving weighted mean algorithm was used to calculate a mean water level over a specified time. The heave correction for each epoch was then the difference between the calculated mean water level and the instantaneous GPS position. The weighting given to each observation was based on the accuracy of the 3D position calculation output from the receiver. Since Kielland and Hagglund’s initial research, improvements to receivers have included:

•    faster update rates – 20 positions a seconds (20Hz);

•    improvements in the algorithms that calculate positions to reject bad observations;

•    faster and more reliable initialisation of roving receivers;

•    time tagging of positions to correct for latency to 5 milliseconds.

Despite the improvements in receiver technology, scepticism about receivers ability to match the manufacturers’ claims while rapidly moving has persisted, although static capabilities have long been proven. Baker (1999) set up a controlled, land based experiment with the 20Hz MS750 RTK-GPS and a TSS DMS-10 heave sensor. The DMS-10 is a heave, pitch and roll sensor designed to be compatible with shallow water multi-beam systems. It is made up of three linear accelerometers and three vibrating gyroscopes that can measure heave at 200Hz within 0.05m and pitch and roll within 0.05° at ±5° (www.intnlind.com/TSS/pr-002.htm). Waves with small amplitudes (0.30m) were simulated and a comparison of the two methods (MS750 and DMS-10) was made. The mean difference between the two methods was 0.05m in amplitude. This improved on the earlier research of Kielland and Hagglund (1995) and was probably due to the higher update rate and more controlled conditions (Figure 4).

Fig. 4: Comparison of MS750 RTK GPS and TSS DMS-10 heave compensator (Baker, 1999).

The most recent testing of the MS750 included the use of an accelerometer and echo sounder in the controlled conditions of a pool (Perwick, 2000). A two second wave with 0.6m amplitude was simulated and heave was measured with a MS750 and TSS 325 heave compensator. The results shown in Table 1 suggest that the MS750 can measure small fast period waves more accurately than the TSS heave sensor.

     10 Hz RTK constant latency              0.019        0.045

     20 Hz RTK constant latency              0.029        0.029

           10 Hz RTK time stamp                   0.025        0.058

Table 1. Standard deviation of heave compensation pool trial (Perwick, 2000)

4.0       Results of Latest RTK GPS Trials

New research has been conducted and confirmed the appropriateness of RTK GPS for hydrographic surveying. Firstly, the vertical accuracy of a Trimble MS750 has been tested while in motion and demonstrated that the receiver works within the manufacturer’s specifications. Secondly, RTK GPS tidal records from various surveys are presented and discussed. Finally a method for precisely aligning depth soundings with GPS heights is shown to overcome problems with data latency.

4.1       Vertical Accuracy of Moving Antenna

The vertical accuracy of most RTK GPS systems operating in synchronised mode is specified to be 2-3cm. Acceptance of these specifications for a stationary GPS is legitimate but further testing was necessary for a receiver in motion. There are various prediction algorithms, based on previous positions within the roving receiver, that help to increase the accuracy and update rate of positions but they can lower accuracy for a receiver when moving. These predictions were found to only slightly degrade accuracy of measurements when the receiver rapidly changes direction. Testing demonstrated that outliers do exist but further processing can remove such effects.

One of the fundamental problems with testing RTK GPS against an accelerometer is the assumption that the accelerometer data is correct. Ground-truthed experiments were necessary to independently measure the accuracy of an RTK system. A purpose built wave simulator (Figure 5) was used to simulate fast period (2.5 second), 0.99m waves. The absolute height of both the top and bottom of the wave motion was positioned with static GPS   surveying as well as by averaging 7-8 minutes of RTK positions.

Fig. 5: 2.5 second, 0.99m wave simulator.

The experiment was quite complex in order to ensure the integrity of the data being collected. A MS750 RTK reference station with v1.06 firmware was set-up using various data output formats (CMR, CMR Plus, CMR 5Hz or CMR 10Hz) via a null modem cable   to a roving MS750 receiver. The CMR (Compact Measurement Record) contains the compressed observations (L1, L2 and pseudo-range), reference station location, antenna height/offset and reference station description (Talbot 1996). CMR Plus is a slightly improved version of the CMR format that has a less peaked throughput (Talbot 1997).  CMR 5 and 10Hz formats are based on the basic CMR message but contains 5 and 10Hz reference station observations. A null modem cable was used to connect the receivers because radios would have introduced extra variables into the testing. Table 2 lists the range of tests undertaken. 

             Low Latency 10 Hz              2.6 second

             Low Latency 20 Hz              3 and 6 second

Table 2. Receiver configurations tested and simulated wave speeds.

The heave measurements of the GPS could then be directly compared to the known motion of the simulator. A variation in the accuracy was observed when using different receiver settings. The conclusions from the tests are:

•    The CMR Plus reference station setting does not show any improvement in accuracy over CMR with this type of testing;

•    the synchronised mode generally yields more precise results  than the low latency mode;

•    results show receiver precision is within the specifications of   the receiver while in motion;

•    spikes were observed at the top and bottom of the antenna motion when using 20Hz setting.

An artefact of the prediction algorithm could be seen where a spike appears at the top and bottom of the wave motion. Figure 6 shows one simulated 20Hz wave with spikes of around 5cm present at the top and bottom of the wave motion. It is however unreasonable to assume that if the raw GPS positions are used for heave correction they will be free of outliers. Many measurement devices including echo sounders, solid state heave sensors and electronic distance measurement (EDM) have some type of filtering, either to smooth the measurements in the case of a heave sensor,  or to remove erroneous measurement in the case of an EDM. It is therefore necessary to fit a cubic spline (Figure 6) to the data using the principles described in mathematical texts such as Press et al (1989). This can be done in real-time during a survey without consuming too much processing power.

Fig. 6: Raw 20Hz RTK GPS Heave smoothed with a cubic spline.

4.2       Tidal Corrections

The University of Waikato has undertaken various surveys using RTK GPS. The tidal records measured from a moving vessel during swell are not as smooth as would be expected from a stationary  tidal station. Figure 7 shows an RTK GPS tidal record from an open ocean navigation channel survey. The averaging period of the tide  was one-minute and there was a significant wave height of 0.6-0.7m. The tidal record appears noisy because the averaging period was too short. The record was then reprocessed with a five-minute averaging period giving a much smoother record.

Figure 8 shows a tidal record measured during beach profile surveys with a significant wave height of 0.5m. Once again the tidal record appears noisy with a three-minute averaging period. When re-sampled with a six-minute period, fluctuations of 3-5cm could still be seen. This was a result of the survey vessel surfing waves while surveying. The vessel spends a longer period of time on the wave crest than in the trough when approaching the beach, thus raising the measured tide level. The opposite is true when the vessel is travelling away from the beach and spends more time in wave troughs. Figure 9 shows a smooth tidal record from a beach survey using a five-minute sampling period, with little swell present. Five minutes is the recommended sampling period when RTK GPS tidal corrections are measured. This length helps to minimise the effect of waves and vessel surfing on the tidal record.

Fig. 7: Tide record from navigation channel survey.

Fig. 8: Tide record from survey of beach profiles.

Fig. 9: Tide record from beach survey – 5 minute sampling period.

4.3       Calibrating of Data Latency

A new calibration method is proposed here which enables precise alignment of WLCs and soundings. Software can approximately correct approximately for latency of GPS positions using a GPS time stamping technique (Trimble, 2000). However, the combined effect of the GPS and sounder latency needs to be compensated for very precisely. Latency needs to be found to the nearest 10 milliseconds for short period waves and 40 milliseconds for longer period waves. The theory behind this method is that when any height of GPS antenna and the associated depth sounding are differenced, the result is a reduced bottom depth that is constant. Therefore, when many soundings and heights are differenced over a constant seabed height while waves are present, the minimum standard deviation of the bottom depths occurs when the latency constant is correct.

The calibration method involved measuring WLCs and depths over a flat seabed while simulating fast period waves. Once the data was collected, the latency constant of the sounder was varied until the error in measuring the bottom depth was minimised. Each trial was based on 60-90s of data or 2000-3000 data points. A total of 15 simulations of 0.8-1m waves were undertaken with a Simrad echo sounder in a 2m deepwater tank. This involved nine trials of 2.5 second period waves, three trials of 5 second period waves and three trials of 7-9 second period waves.

The same trials were repeated with another PC, a different pair of MS750 GPS receivers and an Atlas Deso 14/15 echo sounder off a jetty in 1.5m of water. A total of four simulations were undertaken involving three tests of 2.5-second period, 1m waves and a slower, 7-second period wave. To further strengthen the experiment four simulations of fast period waves were undertaken off a jetty in 3m of water using a Knudsen 320 MP echo sounder.

The latency calibration value was calculated from the fifteen water tank tests. It was very stable with a mean value of 73 milliseconds and a standard deviation of 6 milliseconds. The average of each different wave period simulation is shown in Figure 10. These results highlight how accurate measurement of latency is more important for measurement of short period waves than long. A 50-millisecond change in the latency doubles the error for short period waves, whilst it only has a small impact on longer period waves. This is because a large vertical displacement occurs after a short time with fast period waves.

Fig. 10: Latency calibration graph for Simrad echo sounder.

Figure 11 demonstrates that the latency calibration value was very consistent when using the Atlas sounder too. The average value was 98 milliseconds with a standard deviation of two milliseconds. This longer latency is attributed mainly to the communication rate of the sounder and analogue to digital conversion of soundings. The Atlas works on 4800 bits per second while the Simrad sounder is capable of a higher 19200 bits per second rate. A latency value for a Knudsen 320 MP echo sounder was found to be 26 milliseconds with a standard deviation of two milliseconds.

Fig. 11: 2 second and 7 second trials off a jetty with an Atlas Deso 14/15 sounder.

Two methods of correcting for GPS latency can be used. The first is a constant latency applied to all positions. The second is to correct each position individually using a GPS time stamp method. Perwick (2000) found more precise results when using a constant latency. Experiments to support Perwick’s findings were undertaken by the author but no conclusive results were found. Further testing still needs to be carried out with the specific objective of determining whether a constant latency or GPS time stamping should be used.

Based on experience with the equipment 10Hz is recommended because changes in water level can be accurately measured at this rate, and also because 20Hz doubles the volume of data that needs to be stored and processed. No statistically significant difference was found using 20Hz positions rather than 10Hz.

5.0       Conclusions

The two major issues associated with the use of GPS for measurement of WLCs are timing of data (van Woerden et al, 1986) and accuracy. Both issues have been laid to rest by experiments published in this paper, and earlier by other authors. Latency is the most critical consideration when implementing GPS. A new technique for calibrating data latency within 10 milliseconds has been presented and tested. Sounders from three different manufacturers were trialed and it was demonstrated that the latency calibration value did not vary significantly.

Measuring WLC at the exact location of depth measurements can significantly improve accuracy. Typically tide gauges are located in port or harbour embayments, where the tidal phase and amplitude can be drastically different to the open coast. The variation is exaggerated when tide ranges are large.

The next step for progress of the technology further is to refine the way RTK GPS is implemented in data acquisition and processing software. Three improvement methods are:

• adoption of WLCs;
• filtering of WLCs;
• automated calibration of latency.

Adoption of WLCs firstly requires a change in the hydrographic community’s perception of how soundings are reduced to a datum, followed by new software to support the technique. Filtering of raw WLCs by fitting a cubic spline, or similar method, will further improve the accuracy of corrections. It is possible for the calibration of the equipment latency to be an automated task where the user simulates waves with a GPS and sounder, and software calculates the most likely latency value. Manual calculation is laborious and it is not necessary for every practitioner to learn how it is done.

In the longer term, GPS technology and hydrographic navigation software can be developed to correct for the pitch and roll of a survey vessel. This will not only improve the precision of single beam echo sounder surveys but also offer the opportunity to use GPS to measure the motion of multibeam sounders. In order to measure vessel motion along multiple axes, RTK GPS receivers with a minimum of three antennae are needed. Various authors have discussed the measurement of vessel motion using GPS; they are referenced in Hughes Clack et al (1996). For a more complete discussion of measurement of multidirectional vessel motion see Cooper (1993).

The current practice of measuring tidal and heave corrections separately provides adequate accuracy. However, measuring a WLC will improve the attainable accuracy. RTK GPS is identified as the only available method for making WLC measurements. It has thus been clearly demonstrated that GPS equipment has the ability to measure both WLCs and tide and heave corrections.

References

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Brad Scarfe

is now concluding his Masters of Science at the University of Waikato, New Zealand, majoring in Coastal Earth Science. His final thesis, from which material for this paper is drawn, considers the use of submerged artificial surfing reefs for the protection of eroding coastlines (www.asrltd.co.nz). Prior to this programme of study, Brad spent four  years at the University of Otago completing a Bachelor of Surveying with honours. During his post-graduate studies he has undertaken hydrographic surveys for various environmental projects using RTK GPS. On completion of his  MSc, Brad will be seeking hydrographic work within the field of environmental science.

In the summer of 2000, Brad Scarfe became the first  recipient of a bursary from The Hydrographic Society’s new Educational Award Scheme. The Scheme was designed to assist a student of proven calibre and interest with the costs associated with pursuing an approved programme of study in hydrography   or a related discipline.