Deconvolution Technique to Separate Signal from Noise in Gravel Bedload Velocity Data

A deconvolution procedure is presented to estimate the probability density function of bedload transport velocity from noisy stationary data collected using the bottom tracking feature of acoustic Doppler current profilers (aDcps). The procedure involves the optimization of a computational summation of random variables for the instrument noise (assumed to be Gaussian with zero mean) and the spatially averaged bedload velocity within the insonified area of each acoustic beam (V). The procedure was tested on two aDcp time series, measured in two different gravel-bed rivers (Fraser River and Norrish Creek). Models generated using either a semitheoretical compound Poisson-gamma distribution or an empirical gamma distribution for V were similar and did not differ significantly from the distribution of the original data. Optimized distributions for V were highly positively skewed. The instrument noise was comparable to instrument noise for aDcp water velocity measurements, i.e., an order of magnitude greater than typical bottom tracking noise. The deconvolution procedure presented herein is generally applicable for the difficult measurement problem of determining the actual signal distribution when measurements are contaminated by noise, particularly for the case of positive-valued signal contaminated by Gaussian noise. The procedure produced the first field estimates of spatially averaged bedload velocity distribution.