Optimal Inversion of Manning’s Roughness in Unsteady Open Flow Simulations Using Adaptive Parallel Genetic Algorithm

摘要

Abstract Manning’s roughness coefficient (ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document}) is a comprehensive indicator of flow resistance, and significantly affects the accuracy of one-dimensional (1D) unsteady flow simulations. Most previous studies on roughness inversion have focused on the variation of the ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document} values along the reach—the variations of ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document} with the discharge or water stage have seldom been investigated. To address this issue, an optimization model based on an adaptive parallel genetic algorithm (APGA) is proposed. This model enables better estimations of ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document} in 1D unsteady flow simulations by considering the effects of both distance and discharge on ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document}. The objective of the proposed model is to determine the optimal ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document} values under different discharge strata for every sub-reach by minimizing the discrepancies between the simulated and measured water elevations and discharges. Moreover, a successive-approximation-based stepwise optimizing (SABSO) strategy is developed to improve the performance of the APGA-based optimization model in long natural rivers. The proposed model is evaluated through a case study on the upper reaches of the Yangtze River, China, and compared with models where the ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document} values are considered to vary with distance or discharge. The results show that the APGA with the SABSO strategy yields better solutions than the APGA alone, and that the proposed model outperforms models that do not consider variations of ndocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$n$$end{document} with both discharge and distance. This research provides a novel approach for the inverse estimation of roughness in long river flows.