Long-term continuous acoustical suspended-sediment measurements in rivers - Theory, application, bias, and error

It is commonly recognized that suspended-sediment concentrations in rivers can change rapidly in time and independently of water discharge during important sediment‑transporting events (for example, during floods); thus, suspended-sediment measurements at closely spaced time intervals are necessary to characterize suspended‑sediment loads. Because the manual collection of sufficient numbers of suspended-sediment samples required to characterize this variability is often time and cost prohibitive, several “surrogate” techniques have been developed for in situ measurements of properties related to suspended-sediment characteristics (for example, turbidity, laser-diffraction, acoustics). Herein, we present a new physically based method for the simultaneous measurement of suspended-silt-and-clay concentration, suspended-sand concentration, and suspended‑sand median grain size in rivers, using multi‑frequency arrays of single-frequency side‑looking acoustic-Doppler profilers. The method is strongly grounded in the extensive scientific literature on the incoherent scattering of sound by random suspensions of small particles. In particular, the method takes advantage of theory that relates acoustic frequency, acoustic attenuation, acoustic backscatter, suspended-sediment concentration, and suspended-sediment grain-size distribution. We develop the theory and methods, and demonstrate the application of the method at six study sites on the Colorado River and Rio Grande, where large numbers of suspended-sediment samples have been collected concurrently with acoustic attenuation and backscatter measurements over many years. The method produces acoustical measurements of suspended-silt-and-clay and suspended-sand concentration (in units of mg/L), and acoustical measurements of suspended-sand median grain size (in units of mm) that are generally in good to excellent agreement with concurrent physical measurements of these quantities in the river cross sections at these sites. In addition, detailed, step-by-step procedures are presented for the general river application of the method.

Quantification of errors in sediment-transport measurements made using this acoustical method is essential if the measurements are to be used effectively, for example, to evaluate uncertainty in long-term sediment loads and budgets. Several types of error analyses are presented to evaluate (1) the stability of acoustical calibrations over time, (2) the effect of neglecting backscatter from silt and clay, (3) the bias arising from changes in sand grain size, (4) the time-varying error in the method, and (5) the influence of nonrandom processes on error. Results indicate that (1) acoustical calibrations can be stable for long durations (multiple years), (2) neglecting backscatter from silt and clay can result in unacceptably high bias, (3) two frequencies are likely required to obtain sand-concentration measurements that are unbiased by changes in grain size, depending on site-specific conditions and acoustic frequency, (4) relative errors in silt-and-clay- and sand-concentration measurements decrease substantially as concentration increases, and (5) nonrandom errors may arise from slow changes in the spatial structure of suspended sediment that affect the relations between concentration in the acoustically ensonified part of the cross section and concentration in the entire river cross section. Taken together, the error analyses indicate that the two-frequency method produces unbiased measurements of suspended-silt-and-clay and sand concentration, with errors that are similar to, or larger than, those associated with conventional sampling methods.