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Development of Roughness Updating Based on Artificial Neural Network In Development of roughness updating based on artificial neural network in a river hydraulic model for flash flood forecasting JCFu1,∗, MHHsu2,3 and Y Duann4 1National Science & Technology Center for Disaster Reduction, New Taipei 23143, Taiwan (ROC). 2Department of Civil and Disaster Prevention Engineering, National United University, Miao-Li 36003, Taiwan (ROC). 3Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei 10006, Taiwan (ROC). 4Department Institute of Civil Engineering and Hazard Mitigation Design, China University of Technology, Taipei 11695, Taiwan (ROC). ∗Corresponding author. e-mail: [email protected] 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 based on dynamic wave theory using an implicit finite-difference method is developed with river roughness updating for flash flood forecast. The artificial neural network (ANN) is employed to update the roughness of rivers in accordance with the observed river stages at each time-step of the flood routing process. Several typhoon events at Tamsui River are utilized to evaluate the accuracy of flood forecasting. The results present the adaptive n-values of roughness for river hydraulic model that can provide a better flow state for subsequent forecasting at significant locations and longitudinal profiles along rivers. 1. Introduction which can get better results of forecast (Sene 2013). For example, Liu et al. (2010), Khatibi et al. (2011) Flood forecasting has been an efficient tool for pro- and Park and Markus (2014) used monitored data viding early warning to mitigate the risk of damage (such as daily precipitation, temperature, and river from flash floods. In several countries, the technolo- flow observation) to improve the accuracy of flood gical and procedural improvements have been made modelling with the data assimilation that is avail- to provide early warning message in support of emer- able for flood forecasting. However, simulation gency operation and evacuation. However, there errors were not completely eliminated due to the are still many possibilities to improve the accuracy uncertainties existed in parameters, structure and and computation efficiency of the forecast. boundary conditions of such model. Therefore, sev- Applications of data assimilation techniques eral data assimilation methods had been utilized to (such as input updating, state updating, parameter filter the problems, one of which will be used herein updating and output updating) and the real-time for updating model states (such as water stage and monitoring data arise in the field of real-time flood flow) with observations (Hsu et al. 2010; Weerts forecasting to present an actual state of the system et al. 2011; Neal et al. 2012; Leedal et al. 2013; Keywords. Hydraulic routing; flash flood forecasting; roughness updating; artificial neural network; Tamsui River. J. Earth Syst. Sci. 125, No. 1, February 2016, pp. 115–128 © Indian Academy of Sciences 115 116 JCFuetal. Li et al. 2014). Numerous works have been done can be written as a function to water depth, only to prevent a gradual reduction of the achieved two flow variables, Q and Y ,havetobesolvedin improvement due to lack of parameter updating. equations (1 and 2). Hsu et al. (2006) used observed water stages to Equations (1 and 2) can be solved if the suitable update the roughness of forecasting model based initial and boundary conditions are prescribed. In on the assumption of gradual and varied flow in this work, the four-point implicit finite-difference forecasting. Song et al. (2011) found that the flood approximation (Preissman 1961Amein and Fang routing method with variable parameters presented 1970) is used to solve the equations. During the the relative error of peak discharge less than 20% process of discretization, the two adjoining cross- and runoff volume less than 10% in the Louzigou sections can be organized into two equations with Basin of China. Chen et al. (2013) integrated the four unknown flow variables at the advanced time. Ensemble Square-Root-Filter for parameter opti- mization into a hydrological model to improve real- t+1 t+1 t+1 t+1 t t t t Cℓ Q ,Y ,Q ,Y ,Q +1,Y +1,Q ,Y time streamflow forecasting. Karahan et al. (2013) ℓ+1 ℓ+1 ℓ ℓ ℓ ℓ ℓ ℓ used a hybrid harmony search algorithm to estimate =0 (3) the parameters of the nonlinear Muskingum model. M Qt+1,Yt+1,Qt+1,Yt+1,Qt ,Yt ,Qt Y t The purpose of this work is to evaluate the po- ℓ ℓ+1 ℓ+1 ℓ ℓ ℓ+1 ℓ+1 ℓ, ℓ tential of a river hydraulic model for the real-time =0 (4) forecasting of flash floods with updating the model parameters. Hydraulic model of a river is based where Cℓ and Mℓ are the discretized continuity on dynamic wave theory and an implicit finite- and momentum equations between ℓth and (ℓ+1)th difference method is utilized to provide flood warn- cross-sections, respectively. The subscript ℓ denotes ing information for any desired cross-section of cross-sectional index for 1, 2, ..., L, numbering from rivers. The artificial neural network (ANN) is used upstream to downstream, and t and (t+1) are the to find a simple and efficient roughness updating present and advanced times, respectively. function that the adaptive Manning’s n at each For a river with L cross-sections, a system of time-step of the flood routing process can be deter- (2L−2) equations with 2L unknown flow variables mined by using the previous-time computed flows are obtained. The deficiency in the number of and observed water stages. The river hydraulic equations is compensated by boundary conditions, model with adaptive parameters will be run to which are used to solve for the unknowns. The obtain a better forecasting result that is close to boundary conditions of the dynamic flood routing observed flow data. model are the discharges upstream and the tide stages at the mouth of river. The nonlinear equa- 2. Model tions are solved using Newton’s iteration and the Gaussian elimination methods. 2.1 River hydraulic model Manning friction coefficients are components of the friction slope (Sf ) term for the resistance and Hydraulic model of the river is based on the dy- flow variables from the Manning’s formula namic wave theory of Saint-Venant equations 2 which are continuity and momentum equations n Q |Q| Sf = (5) that describe one-dimensional gradual and varied R4/3A2 flow. These equations are found as follows (Chow where R is the hydraulic radius and n denotes the et al. 1998): roughness of Manning friction coefficient. ∂A ∂Q A fixed Manning’s n may yield poor performance + − q1 + q2 =0 (1) in time-varying dynamic flood routing processes. ∂t ∂x Following the advances in transmission technology, ∂Q ∂ Q2 ∂Y + − gA S − − S real-time observed water stages are obtained from ∂t ∂x A o ∂x f gauge stations and provided new flow information Q that yields the optimal estimate of Manning’s n. −q1V1 + q2 =0 (2) In the work, an ANN is used to update Man- A ning’s n at each time-step of the flood routing pro- where A is cross-sectional area; Y the water depth; cesses in the dynamic flood routing model to ensure Q the discharge; q1 the lateral inflow per unit that the computed water stages are consistent with channel length; q2 the lateral outgoing overflow observations. per unit channel length; So the channel bottom slope; Sf the friction slope; V1 the longitudinal 2.2 Updating roughness based on ANN velocity component of lateral inflow; g the gravita- tional acceleration; t the time; and x the distance An ANN is a parallel computing system which is along the channel. Since the cross-sectional area based on the structure and function of the brain; River roughness updating for flash flood forecasting 117 it is also a computational methodology for solving The effective input, Hj, is passed through a problems by applying information that has been transfer function to generate the outgoing value of gained from past experience to new problems and the node. This transfer function can introduce non- scenarios. Among the many ANN architectures, linearity into ANN models. Commonly used transfer the multi-layer perception architecture is com- functions include linear, sigmoid, and hyperbolic monly applied to make predictions. And a super- tangent functions. Of these three types, the vised learning algorithm is frequently used to teach steadily increasing S-sigmoid function is the most the networks how to input node patterns that are frequently used (Haykin 1999), and the function related to output nodes (Chen et al. 2013; Ryszard values of S-sigmoid are bounded within the range et al. 2014; Uzlu et al. 2014). One hidden layer [0, 1] (Xu and Li 2002). The S-sigmoid function is is used herein to prevent the ANN from falling expressed mathematically as: into bad local minima (Villiers and Barnard 1992). Figure 1 displays the structure of an ANN that con- 1 f(Hj)= . (7) sists of nodes and connections that are organized in 1+exp(−Hj) three layers, i.e., the input layer, the hidden layer, Mathematically, a three-layered ANN with I input and the output layer. nodes, J hidden nodes, and K output nodes can The ANN architecture generally has I input be expressed as: nodes in the input layer, and node j in a hidden J layer that receives information from every node i n = f W O · f(H ) + θO H H k kj j k in the input layer.
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