Modeling point velocity and depth statistical distributions in steep tropical and alpine stream reaches

[1] Statistical hydraulic models predict the frequency distributions of point hydraulic variables, relative to their reach-averaged values, in a stream reach based on its average characteristics (e.g., discharge, depth, width, average particle size). The models initially developed in Europe have not been tested for steeper streams (>4%) with coarse grain size. We recorded water velocities and depths in 44 reaches of steep streams in tropical islands and the Alps during 69 surveys. We fitted the observed distributions of velocities and depths using a mixture of two distributions, one with low variance and the other with a high variance. Then, we predicted the mixing parameter on the basis of the reach-averaged characteristics. We compared the observed and predicted frequencies for five classes of velocities, including a class of negative velocities, and four classes of water depths. The predictions of class frequencies have a bias of ≤5%. Our statistical model of velocity distribution predicts the frequencies of velocity classes with an explained variance between 33 and 72% for four classes of velocity and null for a class of intermediate velocity. The statistical model of depth distributions was less efficient with an explained variance between 25 and 38% for three classes of depth and null for large depths. The average Froude number, the total height of large drops relative to the reach length and the average slope are the main explanatory variables of velocity and depth distributions.