Updated mortality estimation formulae for salmonids passings through Francis turbines at hydropower plants

Downstream migrating fish can be strongly affected by hydroelectric facilities. To set up adapted mitigation measures, it is important to identify these impacts ( e.g. induced mortality rates). For Francis turbines, two mortality prediction formulas, developed in 1989 and updated in 2000, are currently used in France for salmonids according to turbine characteristics and fish size (Larinier and Dartiguelongue, 1989, updated by Bosc and Larinier, 2000). However, their use is limited when some parameters are unknown, such as turbine speed. Moreover, the updated version of can be criticized because of its unpublished development procedure and its unknown predictive power. The main purpose of this study is to update the existing formulae to meet the following objectives: (1) a transparent development procedure, (2) formulae simplification, (3) the use of simple (usually the best-known) turbine parameters, and (4) a maximization of the predictive power and an assessment of prediction errors. Based on data from 73 in situ mortality tests available in peer-reviewed and ‘grey’ literature, we developed two new formulae to estimate salmonid mortality rate in Francis turbines. The first one uses turbine peripheral speed, diameter and fish size (correlation between predicted and observed mortality rates r = 0.89, and root mean square error RMSE = 0.11). The second one is based on usually known parameters: turbine discharge, water head and fish size, to allow a broader applicability ( r = 0.89, RMSE = 0.10). This study comforts the validity of previous formulae and provides two new ones allowing a satisfactory precision in the estimations.