Uncertainty of Index-Velocity Measurements at Culverts

Abstract

The flow through uncontrolled and partly-controlled culverts in environmentally sensitive areas is often monitored based on index-velocity measurements by time-of-travel ultrasonic velocity meters (UVM). Index-velocity monitoring consists of measuring the velocity of the flow in a limited region of the flow cross-sectional area—so-called index-velocities—at time intervals on the order of 15 minutes. Indexvelocities are then used to estimate the mean velocities of the flow using site-specific index-velocity ratings, which are established based on index- and mean-velocity data concurrently measured at the site within the expected range of flows. Water stages are also monitored at the culverts’ ends and, together with the culvert geometry, are used to estimate the flow cross-sectional area. The discharge through the culvert is then computed from the estimated mean velocity and respective flow cross-sectional area. The quality and reliability of index-velocity-based discharge records depends directly upon the measurement uncertainty of the data used for developing the rating and the measurement uncertainty of the indexvelocity and stage data from which the discharges are estimated. To estimate the total uncertainty of index-velocity-based discharge records, the total uncertainty of the index-velocity and mean-velocity measurements of each data pair used for establishing the index-velocity rating need to be estimated first. These measurement uncertainties are then combined for estimating the total uncertainty of the indexvelocity rating throughout the range of index velocities. The rating uncertainties and the uncertainties of the monitored index-velocities and stages from which the discharge record is estimated are subsequently combined to compute the uncertainty of each mean discharge estimate. Moreover, since time-average discharges are typically estimated from measurements collected at time intervals on the order of minutes and the uncertainty of each discharge estimate varies as a function of the flow velocity, the uncertainties of the individual values need to be combined for estimating the total uncertainty of daily, monthly, and annual mean discharges. The evaluation of uncertainty of discharge records is not yet a common practice in flow monitoring. In this paper, we present an evaluation of UVM-measurement uncertainty based on the First-Order Taylor Series Expansion (FOTSE) method for propagation of uncertainty for an uncontrolled culvert site in the South Florida Water Management District (SFWMD). In this evaluation, we show that the precision uncertainty of the index-velocity measurements is not only a function of the frequency of the samples and the sampling time span, but also of the time scale of the turbulence intermittency of the flow. Moreover, we show that since the characteristic time scale is a function of the maximum velocity in the culvert, the precision uncertainty of UVM measurements is a function both the sampling time in the monitoring protocol and the time span over which the data for determining the precision uncertainty are collected.