KHUHWRYLHZOLQNHG5HIHUHQFHV Development of roughness updating based artificial neural network in a river hydraulic model for flash flood forecasting J C FU1,∗, M H HSU2, Y DUANN3 1 National Science & Technology Center for Disaster Reduction, New Taipei 23143, Taiwan (ROC). 2 Department of Civil and Disaster Prevention Engineering, National United University, Miao-Li 36003, Taiwan (ROC). 3 Department Institute of Civil Engineering and Hazard Mitigation Design, China University of Technology, Taipei 11695, Taiwan (ROC). ∗Corresponding author. e-mail: [email protected] Abstract: Flood is the worst weather-related hazard in Taiwan because of steep terrain and storm. The tropical storm often results in disastrous flash flood. To provide reliable forecast of water stages in rivers is indispensable for proper actions in the emergency response during flood. The river hydraulic model is developed with roughness updating at short lead time for flash flood forecast. The river hydraulic model is based on dynamic wave theory using an implicit finite-difference method. The roughness updating using ANN (artificial neural network) is employed to estimate the real-time roughness of rivers at each time-step of the flood routing process. The several typhoon events at Tamsui River are utilized to evaluate the accuracy of flood forecasting. The results present the new n-values of river hydraulic model can provide a better present flow states for subsequent forecasting at significant locations and longitudinal profiles along rivers. Key words. hydraulic routing; flash flood forecasting; roughness updating; artificial neural network; Tamsui River 1. Introduction Flood forecast has been an efficient tool to provide early warning information to mitigate risk of damages from flash floods. In many countries, the technological and procedural improvements have been made to provide early warning information for emergency operation and evacuation. However, despite these advances, there are still many possibilities to reduce time delays of the forecast further and to improve the forecasting accuracy and coverage of the warnings. The data assimilation techniques (such as input updating, state updating, parameter updating and output updating) and real-time monitoring data were integrated into the real-time flood forecasting applications to minimize the difference between computational and observational responses (Sene, 2013). For example, Liu et al. (2010), Khatibi et al. (2011) and Park et al. (2014) used monitoring data (such as daily precipitation, temperature, and river flow data observed) to improve the accuracy of flood model and provide the flood forecasting information. However, simulation errors cannot be eliminated thoroughly due to the uncertainties existed in model parameters, structure and boundary conditions. Therefore, several data assimilation methods had been applied to filtering problems. One of the methods will be used in this research for updating model states (e.g. water stages and flows) with observations (Hsu et al. 2010; Weerts et al. 2011; Neal et al. 2012; Leedal et al. 2013; Li et al. 2014). In order to prevent the improvement from gradually diminishing when one predicts far ahead in time due to lack of parameter updating. Many previous studies have been devoted to addressing this issue. Hsu et al. (2006) used observed water stages as the targets to update roughness based on the assumption of gradual steady and varied flow for the river forecast. Song et al. (2011) described a flood routing method with variable parameters and the results of peak discharge less than 20% in the Louzigou Basin in Henan Province of China. Chen et al. (2013) integrated the Ensemble Square-Root-Filter as parameter optimization into a hydrological model to improve the real-time streamflow forecasting. Karahan et al. (2013) applied a hybrid harmony search algorithm for the parameter estimation of the nonlinear Muskingum model. The objective of the study is to evaluate the potential of a river hydraulic model for real-time flash flood forecasting by updating model parameters. The river hydraulic model was built based on dynamic wave theory using an implicit finite-difference method to provide flood warning information for any desired cross-section including non-gauged stations in rivers. And then the ANN is to find a simple and efficient roughness updating function using previous-time computed flows and observed water stages to update Manning’s n efficiently at each time-step of the ! 1 flood routing process. On the other hand, the river hydraulic model with variable parameters will be run to obtain a better forecasting result fit between computed and observed flow data for short lead time in the study. 2. Model description 2.1 River hydraulic model The river hydraulic model is based on the dynamic wave theory of the Saint-Venant equations which consist of the continuity and momentum equations that describe one-dimension of gradual and varied flow. The equations are found as follows: (Chow, 1973) wA wQ q1 q2 0 (1) wt wx wQ w § Q2 · § wY · § Q · ¨ ¸ gA¨So Sf ¸ qV q ¨ ¸ 0 wt wx ¨ A ¸ wx 1 1 2 A (2) © ¹ © ¹ © ¹ where A is cross-sectional area; Y water depth; Q the discharge; q1 lateral inflow with per unit channel length; q2 lateral outgoing overflow with per unit channel length; channel bottom slope; friction slope; longitudinal S 0 S f V1 velocity component of lateral inflow; g gravitational acceleration; t time; and x distance along the channel. Since the cross-sectional area can be written as a function to water depth, only two flow variables, Q and Y, have to be solved in Eqs. (1) and (2). The solution of Eqs. (1) and (2) can be obtained if the suitable initial and boundary conditions are prescribed. In this work, the four-point implicit finite-difference approximation (Preissman, 1961; Amein and Fang, 1970) is used to solve the equations. During the process of discretization, the two adjoining cross-sections can be organized into two equations with four unknowns of flow variables at the advanced time. t1 t1 t1 t1 t t t t CA QA1,YA1 ,QA ,YA ,QA1,YA1,QA ,YA 0 (3) t1 t1 t1 t1 t t t t M A QA1,YA1 ,QA ,YA ,QA1,YA1,QA ,YA 0 (4) where CA and M A are the discretized continuity and momentum equations between A -th and ( A +1)-th cross-sections respectively. The subscript A denotes cross-sectional index for 1, 2,..., L, numbering from upstream to downstream, and t and (t+1) are the present and advanced times respectively. For a river with L cross-sections, it would indicate a system of (2L−2) equations with 2L unknown flow variables results. The deficiency in the number of equations is compensated with boundary conditions to solve the unknowns. The boundary conditions of the dynamic flood routing model are used as the discharges at upstream and tide stages at the river mouth. The nonlinear equations are then solved using Newton’s iteration method and Gaussian elimination method. Manning friction coefficients are considered as a component of friction slope ( ) term for the resistance and flow S f variables from Manning formula n2Q Q S f (5) R4 / 3 A2 where R is the hydraulic radius and n denotes the Manning friction coefficient. The fixed Manning’s n may generate poor performance during time-varying dynamic flood routing processes. Along with advances in transmission technology, real-time observed water stages are obtained from gauge stations to provide new flow information and yield an optimal estimate of Manning’s n. The study has utilized an ANN to update ! 2 Manning’s n at each time-step of flood routing processes in dynamic flood routing model so that the computed water stages will match observations. 2.2 Roughness updating based ANN An ANN is a parallel computing system which is formed based on structure and function of the brain, and it is a computational methodology that solves problems applying information gained from past experience to new problems and case scenarios. Among the many ANN architectures, multi-layer perception architecture is frequently applied for prediction. For problems prediction, a supervised learning algorithm is frequently utilized to teach the network how to input nodes patterns that can be related to output nodes (Chen et al. 2013; Ryszard et al. 2014; Uzlu et al. 2014). And one hidden layer is used in the study to avoid falling into bad local minima (Villiers and Barnard, 1992). Figure 1 displays the structure of an ANN that consists of nodes and connections organized in three layers, including input layer, hidden layer, and output layer. The ANN architecture generally has I input nodes from input layer, whereas node j in a hidden layer receives information from every node i in input layer. A weight ( H ) and biases ( H ) are linked with each input node (Xi) to Wij Tij node j so that effective incoming information ( ) to node j is obtained from the weighted sum of all incoming H j information I H H H j ¦W ji X i T j (6) i 1 where H and H are the weights and biases between the two respective adjoining layers. Wji T j Input Layer Hidden Layer Output Layer Xi Hj nk Hsinhai B. - Rukou 1 Hsinhai B. 1 Chungcheng B. - Rukou 2 1 | Previous-time Rukou 3 n-values Rukou - Taipei B. 2 Taipei B. - Shizitou 4 nk,t1 Shizitou - River mouth 3 Chungcheng B. Hsinhai B. 2 4 | Chungcheng B. Rukou Difference of water depths Rukou Taipei B. i H k ,t Shizitou Rukou Updated Hsinhai B. k | Taipei B. n-values Chungcheng B. Computed j n Rukou H O k ,t discharges Wji Wkj Taipei B. Qk ,t H O Taipei B. Shizitou T j Tk | Hsinhai B. Shizitou Chungcheng B. Computed water depths Rukou Taipei B.