Test how sampling timing changes a sediment estimate

The pairing of flow and concentration matters

The three schedules contain the same concentration values, rearranged in time. Their arithmetic mean is about 233.33 mg/L. The discharge schedule is unchanged, with mean discharge about 23.33 m³/s at multiplier 1. Yet the paired-bin suspended loads differ: 151,200 kg for aligned peaks and 100,800 kg for early or late peaks.

Predict why before checking the ledger. In the aligned schedule, the largest concentrations coincide with the largest discharges. Multiplication gives those intervals especially large mass rates. Moving high concentrations to lower-flow intervals changes the total even though neither arithmetic mean changes.

Test the mean-product shortcut

A shortcut multiplies mean Q by mean C, then by the full 21,600-second duration and the unit factor 0.001. It gives 117,600 kg for every schedule. Relative to the paired-bin totals, this underestimates the aligned case by 33,600 kg and overestimates the early and late cases by 16,800 kg.

Write the paired products Q × C for each bin on separate cards. Rearrange only the concentration cards while leaving flow cards fixed. Their individual averages remain the same, but the sum of paired products changes. This hands-on rearrangement shows what information the shortcut discards: which concentration traveled with which water volume.

The flow-weighted mean concentration retains that pairing through total mass divided by total water. It is 300 mg/L for aligned peaks and 200 mg/L for early or late peaks at multiplier 1. It is not the same as choosing a concentration observed at the clock-time midpoint.

Challenge a single-sample extrapolation

Another shortcut uses only the first-bin concentration and applies it to the entire six-hour water volume. The aligned first value, 100 mg/L, gives 50,400 kg. The early first value, 400 mg/L, gives 201,600 kg. The late first value, 200 mg/L, gives 100,800 kg, exactly matching that schedule’s paired total.

That last agreement is coincidental in the constructed dataset. The late concentration varies between 100 and 400 mg/L; it is not constant. Its first value happens to equal its event flow-weighted mean. A successful result in one case does not validate the method when the other two provide direct counterexamples.

Capture the three cases and annotate each shortcut as below, above or equal to the paired total. Explain the equality instead of treating it as a reason to discard the mismatches. Reversing which case is inspected first should not change the method evaluation.

Design a sampling plan before seeing the whole event

For a paper plan, assume you do not know which concentration schedule will occur. Choose sampling times that cover rising, high and falling flow rather than only the event’s first hour. State how the plan would pair concentration estimates with discharge over intervals, and what changes more frequent observations could reveal.

Temporal coverage is only one issue. A sample must also adequately represent sediment moving across the channel section. A fixed intake or point sample may require comparison with representative cross-section samples. The browser assumes representative values rather than demonstrating how to obtain them. USGS guidance discusses sampling design and calibration for suspended sediment under changing conditions. USGS automatic-sampling guidance.

An optical or acoustic signal is a surrogate, not automatically concentration in mg/L. A relation to sediment samples needs support and assessment. USGS discussion of acoustic suspended-sediment estimation. No such instrument calibration is performed here.

Separate scaling from a better method

Double the flow multiplier while keeping a timing schedule fixed. True and shortcut loads both double, so their absolute difference doubles while their percentage bias stays unchanged. A larger numerical load does not make the shortcut more representative.

Transfer to two intervals

Two equal one-hour bins have Q values 10 and 30 m³/s and C values 300 and 100 mg/L. Compare the paired load with the product-of-means shortcut. Then swap only the concentrations.

Check the storm-sampling transfer

Initially both mass rates are 3 kg/s, giving 21,600 kg. Mean Q = 20 and mean C = 200 give a shortcut of 28,800 kg. After swapping concentrations, rates become 1 and 9 kg/s, giving 36,000 kg, while the shortcut remains 28,800 kg. The lost pairing explains the changing error.