Considering sampling strategy and cross-section complexity for estimating the uncertainty of discharge measurements using the velocity-area method

Abstract

Summary Streamflow time series provide baseline data for many hydrological investigations. Errors in the data mainly occur through uncertainty in gauging (measurement uncertainty) and uncertainty in the determination of the stage-discharge relationship based on gaugings (rating curve uncertainty). As the velocity-area method is the measurement technique typically used for gaugings, it is fundamental to estimate its level of uncertainty. Different methods are available in the literature ( ISO 748 , Q + , IVE), all with their own limitations and drawbacks. Among the terms forming the combined relative uncertainty in measured discharge, the uncertainty component relating to the limited number of verticals often includes a large part of the relative uncertainty. It should therefore be estimated carefully. In ISO 748 standard, proposed values of this uncertainty component only depend on the number of verticals without considering their distribution with respect to the depth and velocity cross-sectional profiles. The Q + method is sensitive to a user-defined parameter while it is questionable whether the IVE method is applicable to stream-gaugings performed with a limited number of verticals. To address the limitations of existing methods, this paper presents a new methodology, called FLow Analog UnceRtainty Estimation (F laure ), to estimate the uncertainty component relating to the limited number of verticals. High-resolution reference gaugings (with 31 and more verticals) are used to assess the uncertainty component through a statistical analysis. Instead of subsampling purely randomly the verticals of these reference stream-gaugings, a subsampling method is developed in a way that mimicks the behavior of a hydrometric technician. A sampling quality index (SQI) is suggested and appears to be a more explanatory variable than the number of verticals. This index takes into account the spacing between verticals and the variation of unit flow between two verticals. To compute the uncertainty component for any routine gauging, the four most similar gaugings among the reference stream-gaugings dataset are selected using an analog approach, where analogy includes both riverbed shape and flow distribution complexity. This new method was applied to 3185 stream-gaugings with various flow conditions and compared with the other methods ( ISO 748 , IVE, Q + with a simple automated parametrization). Results show that F laure is overall consistent with the Q + method but not with ISO 748 and IVE methods, which produce clearly overestimated uncertainties for discharge measurements with less than 15 verticals. The F laure approach therefore appears to be a consistent method. An advantage is the explicit link made between the estimation of cross-sectional interpolation errors and the study of high-resolution reference gaugings.