Reservoir Bathymetry with a Moving Water Surface
You are responsible for a bathymetric survey of a 3.5 km² hydropower reservoir in Badulla District to estimate siltation since 2010. The reservoir level varies by up to 0.8 m each day because of turbine operation, and there is no tide. You use a single-beam echo sounder (200 kHz) with a 0.35 m transducer draft, RTK GNSS on the vessel, and a shore gauge at the dam read every two hours. Soundings are logged at 5 Hz; the vessel runs at 2.5 m/s, and the GNSS position is time-stamped 0.4 s after the depth sample. The sounder assumes a sound speed of 1,500 m/s, but the water temperature is 28°C and the measured conductivity is low. A preliminary check line crosses the main survey line and shows depths differing by 0.6 m at the same location. The client wants a volume in cubic metres to compare with the 2010 figure and asks whether the result can be guaranteed to ±2%. You have 12,000 soundings, the gauge record, and the RTK vertical precision of 0.05 m.
1. Identify and quantify the main error sources, and explain the 0.6 m check-line discrepancy.
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The largest source is water level: the reservoir moves up to 0.8 m during a day, and a gauge read every two hours may not represent the level at each sounding. If soundings are reduced with a slowly interpolated or fixed level, a 0.6 m apparent depth difference between crossing lines is plausible. The transducer draft of 0.35 m is a constant bias and must be applied. The assumed sound speed of 1,500 m/s will differ slightly from the actual fresh water at 28°C, but that effect is usually small compared with 0.6 m. The 0.4 s position latency at 2.5 m/s gives about 1.0 m along-track position error; on a sloping bed this can also create a depth mismatch where lines cross. RTK vertical precision of 0.05 m is relatively minor.
The check-line discrepancy therefore points first to water-level timing, then to time synchronisation or draft, not to the echo sounder alone.
2. How should the soundings be reduced to a fixed datum and the volume computed with an uncertainty statement?
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Define a fixed reservoir datum. For each sounding, apply the water level at the actual time of the depth sample, interpolated from a reliable gauge record; if the gauge is two-hourly, improve it with a continuous logger or additional readings during turbine changes. Subtract the transducer draft and apply a sound-speed correction based on measured temperature and salinity. Correct positions for the time latency, and reject spikes and bad returns.
Build a TIN or grid from the cleaned soundings and compute volume relative to the datum. Propagate uncertainty from depth, position and water level; report a confidence interval, not a single unqualified number. A 0.1 m depth error over 3.5 km² is already 350,000 m³, so the volume error depends strongly on the mean depth and on the water-level control.
3. The client asks for a guaranteed ±2% volume. What is your response?
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Say that ±2% cannot be guaranteed from the present data. The check-line discrepancy of 0.6 m is much larger than the RTK vertical precision, and the two-hourly gauge is not sufficient for a reservoir that moves 0.8 m per day. To approach ±2%, the survey would need continuous water-level recording, careful time synchronisation, sound-speed and draft checks, repeated check lines, and a documented uncertainty budget.
Offer a defensible volume with an explicit uncertainty range, and explain what additional field work would be needed to tighten it. Do not present a false precision that could mislead the client's siltation comparison.