A modified Simpson model for estimating random uncertainty of moving-boat ADCP streamflow measurements

This paper presents a new analytical model for estimating the random uncertainty of moving-boat ADCP streamflow measurements. The presented model is developed based on the law of propagation of variances. It accounts for an important phenomenon, the dilation of velocity errors due to measurement made on a moving-platform, which is referred to as the 'error dilation' in this paper. The equation of the error dilation is analogous to the well-known time dilation equation in the theory of special relativity. The error dilation increases with increasing the ratio between the boat and water velocities and becomes significant when the ratio is greater than unity. The presented model may be considered as a modified Simpson model that does not account for the error dilation. The presented model helps gain insights into the effects of major parameters or error sources on the measurement uncertainty. The error dilation is confirmed and the presented model is verified with the field data obtained from the moving-boat ADCP streamflow measurements on an irrigation canal in California.