Application of a Novel Arti�cial Neural Network Model in Flood Forecasting

Abstract

flood forecasting. While it is difficult to solve these problems using the empirical 48 statistical model and lumped conceptual hydrological model, since these models 49 usually take the forecast basin as a whole unit and use the area average rainfall as the 50 model input. The distributed hydrological model could solve the problems, but this kind 51 3 of model is complex in structure, complicated in calculation, and requires different 52 types of data (Yu, 2008). 53 Artificial neural network (ANN) is a kind of machine learning technique, and has 54 been widely used in the field of hydrology since 1990s (French et al., 1992;Kang et al., 55 1993; Hjelmfelt and Wang, 1993;Zhu et al., 1994;Hsu et al., 1995;Minns and Hall, 56 1996; Shamseldin A, 1997). The ANN has several mathematical structures, which are 57 able to model highly complicated physical systems (Fotovatikhah et al., 2018), and are 58 more flexible and also a less presumption-dependent method for hydrological systems 59 (Sudheer and Jain, 2004). Artificial neural network techniques are useful for time series 60 modelling and forecasting because they do not require detailed a priori knowledge of 61 the underlying processes (Bruen and Yang, 2005). It has been applied for both rainfall-  The ANN models currently applied in hydrological forecasting is basically the 66 lumped models. In order to solve the complex characteristics of rainfall-runoff process,  In many modelling applications, some traditional hydrological concepts and 75 methods are also integrated into the ANN models to reflect the physical process of 76 rainfall-runoff, Hjelmfelt and Wang (1993) showed that an ANN can be constructed to 77 replicate the unit hydrograph. Jain and Srinivasulu (2006)    The MLP ANN. Such type of ANN generally consists of several layers. Each layer 101 is composed of several parallel neurons. The information is transmitted gradually from 102 the input layer to the output layer through the hidden layer. Each neuron processes 103 received the information from every neuron in the back layer, and outputs the 104 5 information to every neuron in the front layer. Neuron is the information processing 105 unit in the network. Each input of neuron has a parameter weight, and each input 106 multiplies its weight and sums up to get the total value of the input information. When 107 the total input value exceeds the threshold value, the neuron is activated to produce an 108 output. The input information is thus converted to output through an activation function.

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The formula can be expressed as Where o is the neuron output, n is the number of neuron inputs, wi is the weight of input, 112 xi is the neuron input, w0 is the threshold value where x0 = -1, f(x) is the activation 113 function.

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The most commonly used activation functions are sigmoid function, linear 115 function and hyperbolic tangent function. Where,

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The linear function is as follows, The sigmoid function is formulated as follows, For the sigmoid function and hyperbolic tangent function, their maximum value is 121 1 and the minimum value is 0. Therefore, it is necessary to convert the input and output x x Where ' x is the normalized data, max x is the maximum data, min x is the minimum data.

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The back-propagation (BP) algorithms is the widely used training method of MLP 129 ANN (Rumelhart et al., 1986). It is a supervised learning process that adjusts the neuron 130 weight according to the error feedback from the output layer.
Where T t Q  stands for the forecast flow at time instance t+T,  The upstream flow input shall also be considered as an important factor for the 174 river channel that requires forecasting. Similar to the rainfall-runoff process, there is a Where, QOj is the output of layer 4, QOMj is the output after the moving average, nm is 253 11 a parameter.

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In the MLP ANN training, the input and output data is normalized according to 255 formula (4), and the data is also normalized in the ANN model proposed in this paper.

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For the commonly used sigmoid activation function, the maximum output of the ANN  . This correction process iterates many times until the error 281 reaches an acceptable range.  1957, 1960, 1964, 1971, 1975, 1991, 1994 328 and 1995. For the Mozitan and Xianghongdian drainage area, the model is calibrated   than 5%, that is, the absolute value of the error of simulated flood volume is less than 357 15 5%. According to China's norm of hydrological forecasting, the calibrated DC greater 358 than or equal to 0.9 is considered as a class A forecasting model.

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Results of verification are shown in Fig. 8 (simulated in red, observed in black).

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Verification of the model at Mozitan drainage area achieves good performance, where 361 the DC is 0.9 and the NMBE is -2%, while verification of the model at Xianghongdian 362 drainage area achieves poor performance, where the DC is 0.57 and the NMBE is -29%.

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Through the investigation of Xianghongdian basin, it is found that, in year 2018, a 364 rather large water storage was available in the early stage of these projects in the basin, 365 the discharge was increased during the flood period due to the limited storage capacity, 366 and thus the flood peak was increased.

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The uneven spatial distribution of rainstorm is always the problems to be solved       Structure of the ANN model   Simulated (red) and observed (black) discharge of Mozitan and Xianghongdian, model veri cation