Discussion of 'Efficient Algorithm for Computing Einstein Integrals' by Junke Guo and Pierre Y. Julien

摘要

The writers are congratulated for developing analytical approximations to Einstein integrals (herein INT_1 and INT_2). It was stated by the writers in their technical note that these algorithms can be incorporated into professional hydraulic software, and the discussers agree on this. However, it is pointed out here that the calculation of INT_1 and INT_2 can be easily incorporated more directly by subroutines or functions for numerical integration (by using any numerical library or by coding one) into any hydraulic and sediment transport model (e.g., Abad 2002). In terms of practicality, there is a need for more simple formulations than those series-based ones presented by the writers. The present discussion focuses on describing practical formulations for calculating the Einstein integrals based on regression analysis. The development of the methodology is derived for use in depth-averaged sediment transport models.