Question 2 of 5: Ellipsoidally-Referenced (GNSS-Tide) Hydrographic Surveying

Question 2: Ellipsoidally-Referenced (GNSS-Tide) Hydrographic Surveying (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

How it is achieved. In classical hydrography the echo-sounder measures the depth of water below the vessel and a separate tide gauge (plus heave sensor) is used to reduce that depth to chart datum: charted depth = (sounding) − (height of instantaneous water level above datum). The vertical control therefore comes from a water-level observation. In ellipsoidally-referenced surveying (ERS), kinematic GPS (RTK or PPP) continuously fixes the three-dimensional position of the transducer in the geodetic frame — in particular its ellipsoidal height $h_t$ — and the water level is bypassed entirely. The seabed is positioned in the ellipsoidal frame and then transformed to chart datum through a pre-computed separation model (SEP), the height of the ellipsoid above chart datum across the survey area.

Given. A transducer ellipsoidal height $h_t=2.80\ \text{m}$ (positive up), a measured sounding $d=12.50\ \text{m}$ (positive down), and a separation $\text{SEP}=6.30\ \text{m}$ (ellipsoid above chart datum). Find. the charted depth of the seabed below chart datum. With these sign conventions the reduction is obtained directly:

1. Reduce each sounding through the separation model. $$Z_{CD}=d-h_t-\text{SEP}$$ For a transducer ellipsoidal height $h_t=2.80\ \text{m}$, a sounding $d=12.50\ \text{m}$, and a separation $\text{SEP}=6.30\ \text{m}$ (chart datum lies 6.30 m below the ellipsoid): $$Z_{CD}=12.50-2.80-6.30=\boxed{3.40\ \text{m below chart datum}}$$

Because the GNSS height already contains all of the vessel's real-time vertical motion, the same equation simultaneously removes the tide and the heave, roll/pitch-induced heave, squat and settlement — every dynamic vertical effect is absorbed into $h_t$.

Advantages over classical hydrography. (i) No tide gauges and no co-tidal/zoning interpolation — the vertical reference is carried on the boat everywhere, so far-offshore and rapidly-varying-tide areas (estuaries, surge) are handled correctly where a distant gauge would be wrong; (ii) heave, squat, settlement and dynamic draft are eliminated because the GNSS antenna sees the true vertical motion; (iii) results are natively in a 3-D geodetic frame, so soundings can be re-referenced to any vertical datum (chart datum, orthometric, ellipsoidal) after the fact simply by changing the separation model; (iv) it removes the operational cost and failure points of gauge installation and heave-filter tuning.

Limitations. (i) It depends on a reliable, cm-level kinematic GPS height throughout — RTK needs a base within range/telemetry, PPP needs convergence time, and both degrade with satellite geometry (vertical DOP), multipath and signal loss under bridges or high banks; (ii) it needs an accurate separation (SEP) model tying the ellipsoid to chart datum across the whole area — and chart datum (a tidal, physically-defined surface) is itself only known to a few centimetres and can be poorly modelled offshore; (iii) GPS height error maps directly into depth error (no averaging), so a height blunder is a depth blunder; (iv) the lever-arm/attitude (boresight) calibration between antenna and transducer must be precise, since any error propagates fully into the reduced depth.