Extracting settling velocity from optical backscatter data

Optical backscatter (OBS) instruments estimate suspended sediment concentration from the light scattered by particles in water. When a sediment pulse settles, the measured signal usually declines, but that decline is not automatically a settling velocity. It may also reflect tidal transport, turbulent mixing, flocculation, changing particle size, sensor fouling, or a shift in the relationship between optical response and concentration.

A useful calculation therefore begins with a physical description of the deployment. The sensor depth, water-column height, current direction, sampling interval, sediment source, and degree of mixing all affect the result. In a dredging plume near Brisbane or Newcastle, for example, a falling OBS signal may indicate that material has settled locally, or that the ebb tide has carried the plume away from the instrument.

The most defensible workflow converts the optical signal to suspended solids concentration, identifies a period when settling assumptions are reasonable, and then fits a model to the concentration decline. A vertical profile, settling column, or second sensor can substantially reduce uncertainty. The resulting estimate should be reported with its assumptions, calibration range, and quality-control decisions.

Define the signal before calculating velocity

An OBS sensor commonly produces a voltage, count, or digital intensity value related to the amount of light scattered back toward a detector. Some systems describe the measurement as backscatter, while others use optical attenuation or transmission loss. These terms are related but are not interchangeable. Backscatter generally increases with suspended material until the detector approaches saturation; transmitted light decreases as the optical path becomes cloudier.

For a fixed sensor and sediment type, a calibration may take the form:

[ C = aS + b ]

where (C) is suspended solids concentration, (S) is the processed optical signal, and (a) and (b) are calibration coefficients. In some water types, a log-linear or polynomial relationship is more suitable. The calibration must be established with representative sediment, because quartz-rich sand, fine clay, organic particles, and estuarine flocs can produce very different optical responses at the same mass concentration.

The phrase “signal attenuation” should therefore be defined in the data record. It might mean a reduction in transmitted intensity, a decline in backscatter counts after conversion, or an apparent loss of signal caused by fouling. Before fitting a settling curve, inspect raw values, instrument diagnostics, battery status, wiper operation, and any recorded turbidity units. A smooth-looking trace can still be physically misleading if the detector is saturated or the optical windows are coated.

Build a defensible calibration

Collect water samples during the deployment or during a controlled laboratory experiment covering the full expected concentration range. Filter or otherwise process each sample using a consistent gravimetric method, then pair the laboratory suspended-solids result with the simultaneous OBS reading. The calibration should include the particle mixture expected at the site, rather than relying solely on a generic turbidity conversion.

Wavelength is especially important in tannin-stained rivers, blackwater systems, and coastal waters influenced by phytoplankton or dissolved organic matter. Shorter and longer optical wavelengths can respond differently to coloured water and particle composition, so wavelength selection should be considered before interpreting attenuation as sediment removal. In Australia, this matters in systems such as the Fitzroy, tropical wet-season waterways around Cairns, and wetlands receiving dark organic-rich runoff.

Use the calibration only within its validated range. If the instrument records a high-concentration event during dredging near Gladstone or Port Hedland, extrapolating a low-concentration calibration may create an artificial decay rate. Record calibration uncertainty, replicate variability, and whether the samples were collected during rising or falling tide. If sediment mineralogy changes during the event, separate calibrations or particle-size information may be necessary.

Choose a settling model

The simplest model treats a water column as initially mixed and assumes that particles leave through the bed without resuspension. If (H) is the effective water depth and (w_s) is the downward settling velocity, the average concentration can be approximated by:

[ C(t)=C_0\exp\left(-\frac{w_s t}{H}\right) ]

Taking natural logarithms gives:

[ w_s=-H\frac{d(\ln C)}{dt} ]

A straight-line regression of (\ln C) against time therefore produces an estimate of (w_s). The slope must be calculated using concentration, not an uncalibrated voltage, unless the sensor response has been demonstrated to be proportional to concentration over the relevant range. The effective depth may be the mixed layer rather than the total water depth if stratification or a pycnocline limits vertical exchange.

A second approach uses a vertical profile. If concentration changes with depth and time, and horizontal advection and turbulent diffusion are negligible over the analysis window, the one-dimensional conservation equation is:

[ \frac{\partial C}{\partial t} + \frac{\partial (w_s C)}{\partial z}=0 ]

For constant (w_s), this can be solved or simplified according to the observed profile. In an idealised translating sediment front, the front displacement gives (w_s=-dz/dt). In real estuaries, a profile fitted across several depths is usually more reliable than interpreting one fixed sensor because it separates downward movement from general plume dilution.

A settling velocity derived from a concentration decay is an effective or apparent velocity. Flocculation may cause particles to settle faster as concentration changes, while turbulence may hold them in suspension. If a high-tide current reverses during the record, the apparent decline can represent horizontal export rather than vertical deposition. State the model explicitly and avoid presenting a single number as an inherent property of every particle in the sample.

Extract velocity from time and depth

Start by selecting an event with a clear rise and fall in optical response. Remove periods containing sensor start-up effects, bubbles, wiper movement, obvious spikes, and values outside the calibration range. Convert the cleaned signal to concentration, then identify the interval after the sediment input has stopped or become sufficiently stable. Fitting the entire event commonly biases the result because the rising limb reflects transport and source strength rather than settling.

For a mixed-column estimate, calculate (\ln C) for each valid observation and fit a robust linear regression against time. The slope provides (w_s/H), so multiply its negative by the effective depth. Use a depth measured at the time of observation where possible; in tidal channels, water level can change substantially over a few hours. A falling tide in Darwin or a spring-tide cycle in Moreton Bay may make a constant-depth assumption unsuitable.

For a sensor array, align observations by timestamp and check whether the concentration maximum moves downward. If the same feature appears at depths (z_1) and (z_2) at times (t_1) and (t_2), a first estimate is:

[ w_s \approx \frac{z_2-z_1}{t_2-t_1} ]

Use several depths and peaks or percentile levels rather than a single threshold. Cross-correlation between adjacent sensor records can estimate lag, although changing plume shape weakens the result. A profiler can reveal whether a near-bed concentration increase is caused by deposition, resuspension, or a separate inflow; related interpretation methods are described in groundwater flow zones, where vertical changes in water properties likewise need to be separated from sensor and transport effects.

Control field errors

Optical measurements are highly sensitive to bubbles, biofouling, sediment impacts, and the geometry of the deployment. Mount the instrument so it does not sit directly in a bubble stream from a pump, vessel propeller, or breaking surface. In shallow Australian rivers, swimmers, recreational boats, and floating vegetation can create short disturbances that resemble sediment pulses. Flag these observations rather than smoothing them into the settling fit.

Turbulence is a central source of bias. A sensor near a dredge head, discharge pipe, tidal jet, or rock wall may experience a local suspension field that never approaches a simple settling column. Positioning an instrument too close to the bed can also capture resuspension from waves and propeller wash. For a coastal construction project, compare the OBS record with current velocity, water level, wind, and dredging activity. A falling optical signal during strong along-channel flow is weak evidence for deposition unless the horizontal flux is independently assessed.

Instrument maintenance should be part of the analysis plan. Clean optical windows at scheduled intervals, record the cleaning time, and compare pre- and post-cleaning readings. Use dark checks, stable-water checks, and duplicate sensors when the result will support an environmental compliance decision. Australian projects may operate under state approvals such as Queensland’s Environmental Protection Act 1994, New South Wales’ Protection of the Environment Operations Act 1997, or Victoria’s Environment Protection Act 2017; the monitoring method should match the approval conditions and nominated reporting metrics.

Validate and report the result

Validation can use a laboratory settling column, sediment traps, or independently measured particle-size data. In a settling column, take concentration profiles at known times and track the movement of a concentration front or a selected percentile. A trap provides a deposition flux, which can be compared with the integrated loss from the water column, although trap collection is itself affected by turbulence and hydrodynamic bias.

Report the fitted period, water depth, sensor elevation, sampling interval, calibration equation, sediment type, optical wavelength, and excluded data. Include the regression slope, confidence interval, goodness-of-fit, and sensitivity to different start and end times. If the estimate changes from 0.2 millimetres per second to 1.0 millimetre per second when a short storm pulse is removed, that range is more informative than a falsely precise central value.

Interpret the result in the setting where it was collected. Fine cohesive sediment in a calm inland reservoir may have a low effective settling velocity, while flocs in a sheltered estuary can settle rapidly after turbulence falls. Conversely, a tropical cyclone, intense rainfall, or strong vessel traffic can keep material suspended long after the optical peak. In the Murray–Darling Basin, changing river discharge and irrigation return flows may dominate the signal; around the Great Barrier Reef, plume monitoring may need to distinguish natural wet-season sediment delivery from dredging-related concentration changes.

A well-supported estimate connects the optical measurement to a mass concentration, a defined transport model, and an independently plausible settling process. When those links are documented, attenuation data can provide a useful estimate of sediment removal and deposition without confusing optical behaviour with a physical velocity.