Multistep Flood Inundation Forecasts with Resilient Backpropagation Neural Networks: Kulmbach Case Study
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water Article Multistep Flood Inundation Forecasts with Resilient Backpropagation Neural Networks: Kulmbach Case Study Qing Lin *, Jorge Leandro , Stefan Gerber and Markus Disse Chair of Hydrology and River Basin Management, Department of Civil, Geo and Environmental Engineering, Technical University of Munich, Arcisstrasse 21, 80333 Munich, Germany; [email protected] (J.L.); [email protected] (S.G.); [email protected] (M.D.) * Correspondence: [email protected]; Tel.: +49-89-289-23228 Received: 21 October 2020; Accepted: 10 December 2020; Published: 19 December 2020 Abstract: Flooding, a significant natural disaster, attracts worldwide attention because of its high impact on communities and individuals and increasing trend due to climate change. A flood forecast system can minimize the impacts by predicting the flood hazard before it occurs. Artificial neural networks (ANN) could efficiently process large amounts of data and find relations that enable faster flood predictions. The aim of this study is to perform multistep forecasts for 1–5 h after the flooding event has been triggered by a forecast threshold value. In this work, an ANN developed for the real-time forecast of flood inundation with a high spatial resolution (4 m 4 m) is extended to × allow for multiple forecasts. After trained with 120 synthetic flood events, the ANN was first tested with 60 synthetic events for verifying the forecast performance for 3 h, 6 h, 9 h and 12 h lead time. The model produces good results, as shown by more than 81% of all grids having an RMSE below 0.3 m. The ANN is then applied to the three historical flood events to test the multistep inundation forecast. For the historical flood events, the results show that the ANN outputs have a good forecast accuracy of the water depths for (at least) the 3 h forecast with over 70% accuracy (RMSE within 0.3 m), and a moderate accuracy for the subsequent forecasts with (at least) 60% accuracy. Keywords: hazard; artificial neural network; resilient backpropagation; multistep urban flood forecast 1. Introduction Floods are one of the most threatening hazards to civilian safety and infrastructures, causing damages and losses over the world [1]. Especially in densely populated urban areas, urbanization, aging of drainage systems and climate change contribute to growing flood risk in many countries. Ione important mitigation measure is the prediction of future flood occurrences. Real-time flood forecast with sufficient lead time can boost the use of preventive measures for flood mitigation. Such measures can minimize the threats to communities and individuals at risk of flooding [2]. Various types of hydrology and hydraulic models are available for flood forecasting [3]. From the different modeling types, these can be classified into rainfall-runoff models, one-dimensional (1D) model, two-dimensional (2D) model, and coupled 1D–1D model and 1D–2D model. From the forecast application perspective, 2D and 1D–2D models are able to provide directly a spatial surface flood representation, which is essential for flood damage estimation. 1D–1D models, on the other hand, relies heavily on GIS pre- and post-treatments. Most 2D hydrodynamic models are computationally expensive [4]. Even with the help of up-to-date computational techniques for 2D simulations, the computational capability is still inadequate for a real-time forecast [5]. Data-driven is a fast-growing alternative to hydrodynamic models due to the development of computing technologies in recent years. Data-driven models ignore the physical background of a Water 2020, 12, 3568; doi:10.3390/w12123568 www.mdpi.com/journal/water Water 2020, 12, 3568 2 of 20 problem and rather explore the relation between the input and output data [6]. For short or long-term flood forecasts, different data-driven models have been implemented, such as neuro-fuzzy [7], support vector machine [8], support vector regression [9,10], Bayesian linear regression methods [11] and artificial neural network (ANN) [12]. Among them, artificial neural networks (ANN) can be an effective tool for flood modeling, if it is properly applied, overcoming pitfalls as over-fitting/under-fitting with sufficient and representative data for model training [13]. Dawson and Wilby applied ANN to conventional hydrological models in flood-inclined catchments in the UK in 1998 [14]. After that, numerous examinations about flood forecasts in catchment scales emerged [2], [15]. Sit and Demir [16] integrated the river network spatial information to improve the forecast accuracy in Iowa. Bustami et al. applied the backpropagation ANN model for forecasting water levels at gauging stations [17]. ANN showed its great potential on the short-time forecast of extreme water levels with a comparable accuracy to the physical model with a far less computational cost [18]. Simon Berkhahn et al. applied an ANN for two-dimensional (2D) urban pluvial inundation extent forecast [19]. Lin et al. applied backpropagation networks for maximum flood inundation extent prediction and achieved a comparable accuracy to the hydraulic model [20]. The objective of this work is to develop a multistep flood forecast method for urban areas at a fine spatial resolution of 4 m by 4 m. Unlike Lin et al. [20], in this study, an ANN-based framework is proposed for performing multistep forecasts for 1–5 h. To the author’s knowledge, only the works of Chang et al. [2] and Shen and Chang [21] were able to produce multistep flood forecasting maps. The novelty herein is the forecast at a finer resolution of 4 m 4 m, suitable for urban flood forecast. × Our hypothesis is that the ANN forecast model can provide comparably accurate flood extents as hydraulic models, but with a much shorter time of several seconds. As the hydrodynamics-based model runs usually takes several hours, the reduction in forecast time of ANN enables more flood mitigation measures to become effective. In Section2, we introduce the resilient backpropagation artificial neural network structure and the validation of the model. Section3 describes the study area and the data preparation of the event database. Section4 shows the results of flood forecasts of the first intervals for synthetic and historical flood events and the real-time forecast for historical flood events. Sections5 and6 are the discussion and conclusion of this work. 2. Methods 2.1. Data and Structure of Artificial Neural Networks Artificial neural networks are algorithms applied to map features into a series of outputs. Through a structure of the input, output and intermediate hidden layers, artificial neural networks can learn data relationships between input and output data [22]. A feedforward neural network is applied in this work for modeling the study area, proceeding and transmitting data in a network structure [23]. One of the most widely used ANN is the multilayer perceptron (MLP) [24]. The MLP consists of highly interconnected neurons organized in layers to process information. The neurons in one layer are fully connected to each neuron in the next layer. Each connection is then assigned a weight. Each neuron collects values from the previous layer by summing up the results from the previous neuron values multiplying the weight on each input arcs and storing the results on itself. An activation function is used to transfer the results from the hidden layers to the output layer, and a loss function is applied to measure the fit of the neural network to a set of input–output data pair. In this case study, the input layer collects the seven inflows to the urban area of Kulmbach, given the hourly discharge intensity. The output layer is fed with the hourly raster inundation map with a resolution of 4 m 4 m from the event database. Between the input layer and the output layer, × the ANN has 2 hidden layers with 10 nodes per layer. One hundred twenty synthetic events from the event database are used for network training (see Section 3.2). Afterward, the other 60 events in the event database are used for model validation. This represents 2/3 of the date for training and 1/3 for testing, which is often found in the literature [25]. 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