Reverse flow routing in rivers on the rotated x-t plane
WANG Jiabiao1, ZHAO Jianshi1, LEI Xiaohui2, WANG Hao1,2, LIAO Weihong2
1. State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China; 2. China Institute of Water Resources and Hydropower Research, Beijing 100038, China
Abstract：Reverse flow routing is widely used in hydraulic engineering calculations. However, numerical attenuation along the flow direction results in continuously amplified errors when directly solving the hydrodynamic equations in reverse which can lead to unstable calculations. This study contrarotates the x-t plane by 90° from the forward flow position and then derives the reverse flow routing model. On the rotated x-t plane, the initial and boundary conditions for the forward routing model are transformed to the boundary and initial conditions for the reverse model, which avoids the instabilities and non-convergence caused by reverse iterations in time and space. After validation, the reverse model is applied to a real-world case in the Xijiang River. The results show that this model is accurate and stable and can effectively reconstruct the historical inflow hydrographs for various flow cases. This research can improve hydraulic engineering studies using reverse flow routing.
王家彪, 赵建世, 雷晓辉, 王浩, 廖卫红. 基于旋转x-t平面的河渠水流反向演算[J]. 清华大学学报（自然科学版）, 2020, 60(10): 855-863.
WANG Jiabiao, ZHAO Jianshi, LEI Xiaohui, WANG Hao, LIAO Weihong. Reverse flow routing in rivers on the rotated x-t plane. Journal of Tsinghua University(Science and Technology), 2020, 60(10): 855-863.
[1] 钟平安, 李伟, 胡功宇. 河道洪水反向演算问题的研究[J]. 水力发电, 2003, 29(11):3-5, 25. ZHONG P A, LI W, HU G Y. Study on the flood inverse-routing methods in river channel[J]. Water Power, 2003, 29(11):3-5, 25. (in Chinese) [2] 王家彪, 赵建世, 雷晓辉, 等. 基于EnKF的无实测资料区间支流反分析[J]. 水利学报, 2019, 50(10):1189-1199. WANG J B, ZHAO J S, LEI X H, et al. Inverse simulation of ungauged branch inflow based on the EnKF[J]. Journal of Hydraulic Engineering, 2019, 50(10):1189-1199. (in Chinese) [3] 吴晓玲, 王船海, 向小华. 实时校正中的旁侧入流反演方法[J]. 水科学进展, 2009, 20(1):52-57. WU X L, WANG C H, XIANG X H. Inverse analysis of lateral inflow in real-time correction[J]. Advances in Water Science, 2009, 20(1):52-57. (in Chinese) [4] OOI S K, KRUTZEN M P M, WEYER E. On physical and data driven modelling of irrigation channels[J]. Control Engineering Practice, 2005, 13(4):461-471. [5] 彭少明, 郑小康, 王煜, 等. 黄河典型河段水量水质一体化调配模型[J]. 水科学进展, 2016, 27(2):196-205. PENG S M, ZHENG X K, WANG Y, et al. Study on integrated allocation and dispatch model of water quality and quantity for the Yellow River[J]. Advances in Water Science, 2016, 27(2):196-205. (in Chinese) [6] 余真真, 张建军, 马秀梅, 等. 小浪底水库应急调度对下游水污染事件的调控[J]. 人民黄河, 2014, 36(8):73-75, 100. YU Z Z, ZHANG J J, MA X M, et al. Control ranges of emergency dispatches in Xiaolangdi Reservoir for downstream water pollution incidents[J]. Yellow River, 2014, 36(8):73-75, 100. (in Chinese) [7] DOOGE J, BRUEN M. Problems in reverse routing[J]. Acta Geophysica Polonica, 2005, 53(4):357-371. [8] 关志成, 吴海龙, 崔军, 等. 马斯京根法洪水演进反演计算方法的探讨[J]. 水文, 2006, 26(2):9-12. GUAN Z C, WU H L, CUI J, et al. A study on back mathematical calculation procedure of Muskingum method[J]. Journal of China Hydrology, 2006, 26(2):9-12. (in Chinese) [9] 钟平安, 张慧, 邴建平, 等. 河道洪水反流向演算过程迭代方法[J]. 水文, 2007, 27(2):37-39. ZHONG P A, ZHANG H, BING J P, et al. The process iteration method of flood inverse routing in river channel[J]. Journal of China Hydrology, 2007, 27(2):37-39. (in Chinese) [10] BRUEN M, DOOGE J C I. Harmonic analysis of the stability of reverse routing in channels[J]. Hydrology and Earth System Sciences, 2007, 11(1):559-568. [11] KOUSSIS A D, MAZI K. Reverse flood and pollution routing with the lag-and-route model[J]. Hydrological Sciences Journal, 2016, 61(10):1952-1966. [12] 唐文涛, 陆宝宏, 徐玲玲, 等. 基于马斯京根法推求入库洪水计算方法的改进[J]. 水电能源科学, 2012, 30(12):52-54, 215. TANG W T, LU B H, XU L L, et al. Improvement of calculating reservoir flood based on Muskingum method[J]. Water Resources and Power, 2012, 30(12):52-54, 215. (in Chinese) [13] DAS A. Reverse stream flow routing by using Muskingum models[J]. Sadhana, 2009, 34(3):483-499. [14] 李兰. 扩散波的时空反演与洪水实时预报技术[J]. 水文, 1998(6):2-6. LI L. Inverse operation of time-space and real-time flood forecasting for dispersive wave[J]. Journal of China Hydrology, 1998(6):2-6. (in Chinese) [15] ELI R N, WIGGERT J M, CONTRACTOR D N. Reverse flow routing by the implicit method[J]. Water Resources Research, 1974, 10(3):597-600. [16] ABDULWAHID M H, KADHIM K N, ALBAZAZ S T. Inverse flood wave routing using Saint Venant equations[J]. Journal of Babylon University, 2014, 22(1):60-66. [17] D'ORIA M, TANDA M G. Reverse flow routing in open channels:A Bayesian geostatistical approach[J]. Journal of Hydrology, 2012, 460-461:130-135. [18] 王尧, 李兴凯, 王建群. 基于模拟退火粒子群算法的河道洪水反流向演算[J]. 水文, 2012, 32(6):6-10. WANG Y, LI X K, WANG J Q. River flood inverse-routing based on simulated annealing particle swarm optimization[J]. Journal of China Hydrology, 2012, 32(6):6-10. (in Chinese) [19] ZUCCO G, TAYFUR G, MORAMARCO T. Reverse flood routing in natural channels using genetic algorithm[J]. Water Resources Management, 2015, 29(12):4241-4267. [20] 刘欢, 陆宝宏, 陆建宇, 等. 基于BP神经网络模型的河道洪水反向演算研究[J]. 水电能源科学, 2016, 34(3):52-54. LIU H, LU B H, LU J Y, et al. Study on flood inverse-routing in river channel based on BP neural network[J]. Water Resources and Power, 2016, 34(3):52-54. (in Chinese) [21] SZYMKIEWICZ R. Application of the simplified models to inverse flood routing in upper Narew river (Poland)[J]. Publications of the Institute of Geophysics, Polish Academy of Sciences, 2008, E-9(405):121-135. [22] 王船海, 李光炽, 向小华, 等. 实用河网水流计算[M]. 南京:河海大学出版社, 2003:61-72. WANG C H, LI G C, XIANG X H, et al. The practical flow calculation in river-net[M]. Nanjing:Hohai University Press, 2003:61-72. (in Chinese) [23] PAPPENBERGER F, MATGEN P, BEVEN K J, et al. Influence of uncertain boundary conditions and model structure on flood inundation predictions[J]. Advances in Water Resources, 2006, 29(10):1430-1449. [24] 王家彪. 西江流域应急调度模型研究及应用[D]. 北京:中国水利水电科学研究院, 2016. WANG J B. Research and application of reservoir system emergency operation model in Xijiang River basin[D]. Beijing:China Institute of Water Resources and Hydropower, 2016. (in Chinese) [25] ZHANG J H, CHEN L, SINGH V P, et al. Determination of the distribution of flood forecasting error[J]. Natural Hazards, 2015, 75(2):1389-1402. [26] ZHAO T T G, ZHAO J S. Forecast-skill-based simulation of streamflow forecasts[J]. Advances in Water Resources, 2014, 71:55-64. [27] 赖锡军. 水动力学模型与集合卡尔曼滤波耦合的实时校正多变量分析方法[J]. 水科学进展, 2009, 20(2):241-248. LAI X J. Real-updating multivariate analysis for unsteady flows with ensemble Kalman filter[J]. Advances in Water Science, 2009, 20(2):241-248. (in Chinese)
2020, Vol. 60 
