Application of a novel artificial neural network model in flood forecasting

In this paper, a novel ANN flood forecasting model is proposed. The ANN model is combined with traditional hydrological concepts and methods, taking the initial Antecedent Precipitation Index (API), rainfall, upstream inflow and initial flow at the forecast river section as input of model, and flood flow forecast of the next time steps as output of the model. The distributed rainfall is realized as the input of the model. The simulation is processed by dividing the watershed into several rainfall-runoff processing units. Two hidden layers are used in the ANN, and the topology of ANN is optimized by connecting the hidden layer neurons only with the input which has physical conceptual causes. The topological structure of the proposed ANN model and its information transmission process are more consistent with the physical conception of rainfall-runoff, and the weight parameters of the model are reduced. The arithmetic moving-average algorithm is added to the output of the model to simulate the pondage action of the watershed. Satisfactory results have been achieved in the Mozitan and Xianghongdian reservoirs in the upper reaches of Pi river in Huaihe Basin, and the Fengman reservoir in the upper reach of Second Songhua river in Songhua basin in China.


Introduction
Accurate flood forecasting is important for flood control and disaster reduction and prevention. Therefore, various hydrological models for flood forecasting have been developed in history. These models can be classified into three major types: empirical statistical model, lumped conceptual hydrological model and distributed hydrological model. However, difficulties in the long-term practice of flood forecasting exist due to the complexity of the rainfall-runoff process in a watershed. The heterogeneity of spatial distribution of rainfall always has been an important factor affecting the accuracy of flood forecasting, while it is difficult to solve these problems using the empirical statistical model and lumped conceptual hydrological model, since these models usually take the forecast basin as a whole unit and use the area average rainfall as the model input. The distributed hydrological model could solve the problems, but this kind of model is complex in structure, is complicated in calculation, and requires different types of data (Yu, 2008).
The ANN models currently applied in hydrological forecasting are basically the lumped models. In order to solve the complex characteristics of the rainfall-runoff process, efforts have been made in many researches to use ANN model combinations to establish forecasting models. Zhang and Govindaraju (2000) used a set of parallel ANN models to deal with rainfall-runoff simulation of different magnitude (low, medium, and high magnitudes). According to the different influencing factors and laws of the runoff process, such as flood, recession, and base flow, Jain and Srinivasulu (2006) used several parallel ANN models to simulate different parts (segments) of runoff hydrograph, i.e., baseflow, rising limb and falling limb, etc.
In many modelling applications, some traditional hydrological concepts and methods are also integrated into the ANN models to reflect the physical process of rainfall-runoff. Hjelmfelt and Wang (1993) showed that an ANN can be constructed to replicate the unit hydrograph. Jain and Srinivasulu (2006) demonstrated that the infiltration and the effective rainfall could be computed by simply subtracting the incremental infiltration from the total rainfall for ANN modelling. Corzo and Solomatine (2007) used baseflow separation techniques for ANN modelling in flood forecasting.
Most of ANN models used for hydrological forecasting are of the classical multi-layer perceptron (MLP) type. In recent years, new types of ANN models have also been used in hydrological forecasting, such as the extreme learning machine (Yaseena et al., 2019) and support vector machine and artificial neural network (Bafitlhile & Li, 2019). Herbert et al. (2021) applied the deep learning algorithms and encoder-decoder algorithm in ANN to predict the long-term reservoir inflow. Sawaf et al. (2021) used a recurrent neural network (RNN) model of two hidden layers to provide forecasting of river flow during flood events.
Since ANN models have the ability to simulate highly complicated physical systems and are more flexible in structure while not requiring more different types of data, we try to use the ANN model to solve problems of the heterogeneity of spatial distribution of rainfall in flood forecasting. The ANN model is combined with traditional hydrological concepts and methods, and the key factors affecting runoff formation are taken as model inputs according to the physical process of rainfall-runoff. By optimizing the topology of ANN, distributed rainfall is realized as the input of the model. A flood forecasting ANN model is thus developed to forecast the flow in future, which requires not much data, is easy to use in realtime flood forecasting and is expected to have good accuracy in flood forecasting.

Introduction of multi-layer perceptron
The proposed ANN model in this paper is based on the multi-layer perceptron (MLP)-type ANN model.
The MLP ANN. Such type of ANN generally consists of several layers. Each layer is composed of several parallel neurons. The information is transmitted gradually from the input layer to the output layer through the hidden layer. Each neuron process receives the information from every neuron in the back layer, and outputs the information to every neuron in the front layer. The neuron is the information processing unit in the network. Each input of neuron has a parameter weight, and each input multiplies its weight and sums up to get the total value of the input information. When the total input value exceeds the threshold value, the neuron is activated to produce an output. The input information is thus converted to output through an activation function. The formula can be expressed as where o is the neuron output, n is the number of neuron inputs, w i is the weight of input, x i is the neuron input, w 0 is the threshold value where x 0 = − 1. f is the activation function.
The most commonly used activation functions are sigmoid function, linear function and hyperbolic tangent function.
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 1 and the minimum value is 0. Therefore, it is necessary to convert the input and output samples of the network to the values of interval [0,1], which is called normalization processing. A number of normalization methods are available in practice. The most commonly used method is the proportional compression that can be expressed as where x ′ is the normalized data, x max is the maximum data and x min is the minimum data. The back-propagation (BP) algorithm is the widely used training method of MLP ANN (Rumelhart et al., 1986). It is a supervised learning process that adjusts the neuron weight according to the error feedback from the output layer.

Key influencing factors of runoff generation
The antecedent soil moisture and the rainfall process, the changes of antecedent baseflow of a watershed and the inflow process of upstream channel are key factors affecting the rainfall-runoff process of a watershed outlet. Conceptual hydrological models based on the physical concept of rainfall-runoff, e.g. the Xinanjiang model (Zhao, 1992) and Sacramento model (Burnash, 1995), are still effective and commonly used models in operational rainfall-runoff forecasting. The inputs of these models mainly include the antecedent soil moisture, rainfall process, evaporation and baseflow of a watershed. Wu and Chau (2011) proposed the input of an ANN which is similar to that of a conceptual model. It can be formulated as follows: where Q t+T stands for the forecast flow at time instance t + T, Q t+1−l 1 is the antecedent flow (up to t + 1 − l 1 time steps), P t+1−l 2 is the antecedent rainfall (up to t + 1 − l 2 time steps), S t+1−l 3 (up to t + 1 − l 3 time steps) represents any other factors contributing to the true flow Q t+T such as evaporation or temperature and l 1 , l 2 and l 3 stand for the number of previous flow, rainfall and other factors respectively.
In this paper, S (in Eq. 5) is replaced by the parameter of soil tension moisture in the conceptual model. The Antecedent Precipitation Index (API) of the API model (Linsley et al., 1975), the most simple and effective index, is used to calculate the parameter of soil tension moisture. The API has been used as an input of the recurrent neural network model in flood forecasting (Sawaf et al., 2021). The calculation formula of API in the hydrological forecasting is as follows: where API t+1 stands for the API at time instance t + 1, API t stands for the API at time instance t, P t stands for the rainfall in time interval from t to t + 1, K is a parameter with different values for the different months and IM is the maximum value of API.
The unit hydrograph method (Sherman, 1932) has been widely used in real-time flood forecasting for a long time. The basic concept of the unit hydrograph is that a period of effective rainfall forms a flow process Fig. 1), where τp is the period of time when the flood peak of unit hydrograph, i.e. the time from the start of rainfall to the emergence of flood peak at the basin outlet, appears. Based on this theory, the flow at time t is converted by the convolution of effective rainfall before time t, where the runoff generated by rainfall before time t-τp has entered the stage of recession, and the runoff converted by rainfall after time t-τp is at the stage of rising. Therefore, the rainfall process from t-τp to t is selected as the rainfall input, and these rainfall inputs are converted into runoff in a watershed. Accordingly, API selects the value at time t-τp as the commencement of the rainfall-runoff calculation, while the runoff converted by rainfall before t-τp is accounted in the flow recession or baseflow by Q t-τp , as the input of the flow recession. The formula is where QO t stands for the forecast flow at time instance t, API t-τp is the API at time instance t-τp, Δt is the time step of forecasting, P t-τp+Δt and P t are the precipitation at time step [t-τp, t-τp + Δt] and [t-Δt, t] and Q t-τp is the flow at time instance t-τp.
The upstream flow input shall also be considered as an important factor for the river channel that requires forecasting. Similar to the rainfall-runoff process, there is a peak time τq in the unit hydrograph, that is, the time from the upstream pulse inflow to the outlet peak flow of the basin. River flow routing is in general faster than that of the overland flow, so it usually shows τq < τp. The formula can be expressed as where QU t-τq , QU t-τq+Δt and QU t are the inflow of the upstream section at time instances t-τq, t -τq + Δt and t, respectively.

The novel artificial neural network
Commonly, the MLP ANN has one hidden layer. Kia et al. (2012) developed a two-hidden layer MLP model; the flood level is simulated with rainfall, slope, elevation, flow accumulation, soil and land use as input. Sawaf et al. (2021) used a recurrent neural network (RNN) model of two hidden layers to provide flood flow forecasting. In this paper, based on the concept of deep learning, one more hidden layer is used to reflect the physical conceptual process of runoff generation and watershed concentration. The ANN is divided into four layers (see Fig. 2). Starting from the bottom to the top, the first layer (l 1 ) is the input layer, the second layer (l 2 ) and third layers (l 3 ) are the hidden layers that simulate the rainfall-runoff generation and watershed concentration and the fourth layer (l 4 ) collects all runoff to the catchment outlet. In addition, an arithmetic moving-average (MA) processing is applied in the front of the layer 4. In the MLP ANN, each neuron receives information from every neuron in its back layer. In this paper, to accommodate the large number of distributed rainfall input, the topological structure of ANN is optimized to reduce those unnecessary neuron connections without physical meaning; therefore, the input weight parameters that require calibration are substantially reduced to achieve effective training of ANN with two hidden layers and many neurons. Distributed rainfall input is processed by dividing the watershed into several rainfall-runoff processing units. In each unit area, the rainfall-runoff process is only affected by the soil moisture and rainfall within the unit; it is not affected by the upstream flow, the soil moisture and rainfall from other units. Similarly, the calculation of upstream flow routing is not affected by the rainfall and other factors within the units. Based on the concept of deep learning convolutional neural network (Krizhevsky et al., 2012) feature map, the 1-3 layers of the artificial neural network are divided into several groups as shown in Fig. 2. From Fig. 2, the groups on the left side simulate the rainfall-runoff generation and flow concentration within the area of each rainfall-runoff processing unit. Groups on the right side simulate the flow routing of the upstream river and the recession of baseflow from left to right respectively. Different from the feature map, the neurons in these groups are only connected to the neurons in the front layer of the same groups respectively.
Regarding the group of rainfall-runoff simulation, in the first (input) layer, neurons from left to right in Fig. 2 are the initial soil moisture (API t-τp ) at the time (t-τp) when the rainfall-runoff process commence in the rainfall-runoff processing unit and the number of p Δt rainfalls (P t-τp+Δt , P t-τp+2Δt ,…P t-Δt , P t ) from the time t-τp when the rainfall-runoff commence in the processing unit to the time t, respectively. The total number of inputs is p Δt + 1 . The second layer simulates the runoff generation in the processing unit. There are a total number of p Δt neurons representing a total number of p Δt runoffs (R t-τp+Δt , R t-τp+2Δt ,…R t-Δt , R t ) generated by rainfall within the processing time period. The neurons of the second layer are only connected with that of the first layer within the processing time period in the same processing unit (see the Fig. 2), i.e. the runoff generation at a certain time is only affected by the soil moisture at the initial time and the rainfall before that time in the same processing unit, but not by the rainfall after that time in the same processing unit and rainfall in other processing units. The third layer collects the runoff at each time step to simulate the runoff within the processing unit at the time t.
Regarding the group of upstream flow routing, in the first (input) layer, neurons from left to right in Fig. 2 are the upstream flow input (QU t-τq , QU t-τq+Δt ,…QU t-Δt , QU t ) from time t-τq to time t, with a total number of q Δt + 1 input neurons. The second layer simulates river flow routing, with a total number of q Δt + 1 neurons representing the contribution of a number of q Δt + 1 flow input to the watershed outlet section at the time t. Similar to the rainfall-runoff simulation, neurons in the second layer are only connected with the neurons in the first layer at the  Fig. 2). In the third layer, the flow at each time step is routed to the outlet section of the watershed.
Regarding the group of flow recession, in the first (input) layer, one neuron input is the discharge (Q t-τp ) at the outlet section of the watershed at the time t-τp. This input neuron is connected to a neuron in both the second and third layers. The recession runoff process generated by rainfall and upstream flow before the time t-τp in the watershed is thus simulated throughout this group.
Natural watershed has good pondage action on runoff. The water storage increases when the runoff in the watershed arises, and the water storage decreases when the runoff in the watershed drops. The runoff hydrograph is smoothed by normalizing the runoff process. The conceptual hydrological forecasting model often uses the function of storage to simulate the pondage action in a watershed. The ANN model lacks the storage and regulation function for the rainfall input. The output of the model has a quick response to the input, which often brings sharp and rough fluctuation in the simulated hydrograph. To make up for such shortcoming of the ANN model, the arithmetic moving average process (layer MA) is applied before the neuron output, and the forecast flow is obtained by averaging the output of several time steps, that is, where QO j is the output of layer 4, QOM j is the output after the moving average and nm is a parameter.
In the MLP ANN training, the input and output data is normalized according to Formula (4), and the data is also normalized in the ANN model proposed in this paper. For the commonly used sigmoid activation function, the maximum output of the ANN will not exceed the value "1" since the function has a restricted output interval of [0, 1]. Thus, in real-time forecasting no matter how large the actual input value is, still the simulated flow after rescaling cannot exceed the maximum value of the training data set. This is unreasonable in real situations. Moreover, since the sigmoid activation function has an "S" shape, the function curve tends to be flat with the increase of input value, which does not conform to the law of rainfall-runoff in practice, and is difficult to accurately simulate floods of different magnitudes. The maximum value of the output of a linear function can exceed the value "1", which better conforms to the law of the rainfall-runoff process. Therefore, the linear function is chosen as the activation function of ANN in this paper.
The training algorithm in this paper is the commonly used back-propagation (BP) algorithms. The input weight (w) of the neuron is calibrated iteratively through the supervised training based on measurement data. The learning process consists of two parts, that is, the forward propagation of signals and the backward propagation of errors (δ). In the forward propagation, the signal propagates upward, and the input data comes from the input layer and then output after being processed through layer 2, layer 3, layer 4 and the moving average algorithm (layer MA). Different from the BP algorithms of MLP, the error propagates backward from the output to layer 4 (l 4 ) by bypassing the moving average algorithm (layer MA), as shown in Fig. 3. The errors of neurons in the layer "l + 1" are multiplied by the input weight (W i ) and allocated to the connecting neurons of the layer l (δ li = δ l+1 × W li ). The input weight (W l−1 ) of each neuron in layer l − 1 connecting to the layer "l" is adjusted according to the neuron errors in layer l. The weight is adjusted by the gradient descent method. The amount of adjustments is ΔW l−1,i = − l W l−1,i This correction process iterates many times until the error reaches an acceptable range.

The data
The study areas are the Mozitan and Xianghongdian reservoirs in the upper reaches of Pi River in Huaihe Basin, and the Fengman reservoir in the upper reach of the Second Songhua river in Songhua Basin in China. Pi River is located at about 31° north latitude with a warm temperate climate in Anhui province in east China. It is a humid region and a mountainous area with a good vegetation coverage. The annual precipitation is about 1500 mm, of which about 60% falls in the rainy season (from May to September), and most of the storm floods occur from June to August. Upstream of the Second Songhua river is located about 43° north latitude with a cold temperate climate in Jilin province in northeast China. It is 1 3 Vol.: (0123456789) a semi-humid region and a mountainous area with a good vegetation coverage. The annual precipitation is about 750 mm, of which 70% falls in the rainy season (from June to September), and most of the storm floods occur in July and August.
The most widely applied rainfall data in real-time flood forecasting which can be easily obtained from observation stations is used as the input of the model. It is the same as the traditional API and Xinanjiang model of these river basins; the time step of the flood forecasting model developed in this paper is 1 or 6 h, which is commonly used in China. The locations of Mozitan and Xianghongdian reservoirs, its river networks, and hydrological monitoring stations are shown in Fig. 4. The Mozitan drainage area is 570 km 2 , which is divided into 4 rainfall-runoff processing units in compliance with the 4 precipitation stations. The Xianghongdian drainage area is 1431 km 2 , which is divided into 6 rainfall-runoff processing units in compliance with the 6 precipitation stations. The location of the Fengman reservoir, its river networks and its monitoring stations are shown in Fig. 4. The Fengman reservoir drainage area is 11,900 km 2 , which is divided into 11 rainfall-runoff processing units in compliance with its 11 precipitation stations. Data from these precipitation stations are used. The model inputs are the API at the initial time of each rainfall-runoff processing unit, the number of p Δt interval rainfall of every processing unit and the flow at the initial time of forecast hydrological station. In addition, there are a number of ( q Δt + 1 ) of outflow for the Baishan reservoir and flow of the Wudaogou station for the Fengman drainage area. The calculation method, the parameters of API and the determination of τp can refer to the existing traditional hydrological forecasting scheme. There are several different unit hydrographs available for these watersheds, and the maximum value of the different unit hydrograph in the respective watershed is chosen as the parameter τp for each watershed, where τp is 4 h for the Mozitan drainage area, 9 h for the Xianghongdian drainage area and 48 h for the Fengman drainage area. The τq of the Fengman drainage area is 6 h. Like the existing API models, the API in this paper is calculated from 1st April for Mozitan and Xianghongdian, and from 1st May for Fengman, i.e. 1 month before the rainy season. Similarly, like the existing API and Xinanjiang models, the time step of the developed ANN model calculation is 1 h for Mozitan and Xianghongdian, and 6 h for Fengman. For the Mozitan drainage area, there are 4 rainfall-runoff processing units; each unit has 1 API and 4 time periods of rainfall input, as well as one initial flow input of the prediction section. For the Xianghongdian drainage area, there are 6 rainfall-runoff processing units; each unit has 1 API and 9 time periods of rainfall input, as well as one initial flow input of the prediction section. For the Fengman drainage area, there are 11 rainfall-runoff processing units; each unit has 1 API and 8 time periods of rainfall input, each 2-flow input of Wudaogou and Baishan and 1 initial flow input of the prediction section.
The models of the Mozitan and Xianghongdian drainage areas are calibrated using large-scale flood data in the history of recent years, 2012, 2013, 2014 and 2016 with a total number of 837 data sets of the API, rainfall and initial flow for the Mozitan, and years 2012Mozitan, and years , 2013Mozitan, and years , 2014Mozitan, and years , 2015 and 2016 with a total number of 676 data sets for the Xianghongdian. The historical flood data of the years 1957, 1960, 1964, 1971 and 1975 are adopted for the Fengman drainage area, and 972 sets of the API, rainfall, flow and initial flow data are used for model calibration.
Recently, the Mozitan and Xianghongdian drainage areas experienced flood events. There are floods in the years 2018 and 2020 for Mozitan, and flood in the year 2018 for Xianghongdian. Data of these flood events were used to verify the model, i.e. to obtain the forecasts from the calibrated model, with a total number of 1154 data sets of the API, rainfall and initial flow for Mozitan and 65 data sets for Xianghongdian. In contrast, since there was no major flood in the Fengman basin after year 2000, 600 data sets of the API, rainfall and flow from 1991, 1994 and 1995 were used to verify the model for Fengman.

Results
The ANN model was trained by the input historical flood data, i.e. the automatic calibration. During the training, the parameter nm of pongde action in the simulated basin needs to be manually adjusted according to experience and calibrating results, and then restart the model training until the calibration is completed.
The performance of the model in this study was evaluated using two different standard statistical measures. The normalized mean bias error (NMBE), measuring the error of the simulated flood volume, is an important indicator for the accuracy of reservoir inflow flood forecasting. The Nash coefficient (Nash & Sutcliffe, 1970), i.e. deterministic coefficient (DC), measures the degree of coincidence between the modelling process and the actual measurements of the flood process. The calculation formulas of the NMBE and DC are as follows: where QOM(t) is the calculated flow from the model at time t, Q(t) is the observed flow at time t, EQ is the average value of the observed flow and N is the number of flow records in a time period. For the model calibration, simulated and observed discharges at the Mozitan and Xianghongdian stations of Pi River are shown in Figs. 5 and 6 respectively (simulated in red, observed in black). The DC and NMBE of simulation results are 0.90 and 1.8% for the Mozitan and 0.91 and 5% for the Xianghongdian, respectively. The simulated and observed flows of model calibration at the Fengman station of Second Songhua River are shown in Fig. 7 (simulated in red, observed in black). The DC and NMBE of the simulation results are 0.93 and − 0.8% respectively. According to China's norm of hydrological forecasting, the calibrated DC greater than or equal to 0.9 is considered as a class A forecasting model.
Results of the verification of Mozitan, Xianghongdian and Fengman stations are shown in Figs. 8, 9 and 10 (simulated in red, observed in black), respectively. Verification of the model at the Mozitan and Fengman drainage areas achieved good performance, whose DC and NMBE are 0.89 and 6.7% for Mozitan and 0.83 and 2.6% for Fengman, respectively, while verification of the model at the Xianghongdian drainage area achieves relatively poor performance, where the DC is 0.57 and the NMBE is − 29%. Through the investigation of the Xianghongdian basin, it is found that, in year 2018, a rather large water storage was available in the early stage of these projects in the basin, the discharge was increased during the flood period due to the limited storage capacity and thus the flood peak was increased.
The uneven spatial distribution of rainstorm is always the problem to be solved in flood forecasting. The ANN rainfall-runoff operational model developed in this paper uses distributed precipitation and API as model input, and simulates runoff by dividing rainfall-runoff processing units, which can better solve this problem. It is useful in flood forecasting, especially for watershed where the heterogeneity of spatial distribution of rainfall is noteworthy. As shown in Figs. 0.5-10, the model achieves good simulation and verification accuracy, and is suitable for flood events at different magnitudes.

Discussion
In the ANN model proposed in this paper, neurons of the hidden layers (l 2 , l 3 ) are only connected with the neurons of the back layer with physical conception relations. It reduces the number of weight parameters (W) that needs to be trained. There are 6 rainfallrunoff unit areas in Xianghongdian; each has 1 API and 9 rainfall input time periods. There are 60 inputs from 6 unit areas, and 1 channel baseflow input in addition. Therefore, the ANN model has 387 weight parameters in total, while there would be about 3747 weight parameters if each neuron in the back layer is connected with all the neurons in the front layer according to traditional MLP ANN connections. The neuron connections proposed in this study not only reduces the weight parameters, but also eliminates the connections of the input without physical conceptual causes. It can produce more reasonable values of weight parameters and avoid pure mathematical fitting without physical causes.
In some ANN with multiple hidden layers, the top two layers can easily overfit the training set; training errors do not necessarily reveal the difficulty in optimizing the lower layers (Erhan et al., 2010). Therefore for example, dropout (Srivastava et al., 2014) and others promoted several methods to solve this problem. In the ANN proposed in this paper, compared with the initial values, the weight parameters of each layer trained by the traditional BP learning algorithms are significantly improved. This can be due to the optimized connection of hidden layer neurons, which makes the error backward propagation more effective. Generally, an initial value needs to be given before the parameter calibration starts. One disadvantage of the gradient descent method is that it cannot guarantee the convergence of parameters to the optimal solution, especially when the initial value is set unreasonably. Therefore, the initial value of the weights should be set at a reasonable value, such as a small positive figure.
Pondage action of the basin reflects the increase and decrease of the water storage in a basin with the  Conceptual hydrological models such as the Xinanjiang model (Zhao, 1992) and Sacramento model (Burnash, 1995) often use free water tank regulation to simulate pondage action. In the ANN model, the input information is instantaneously echoed by the output accordingly. In the absence of pondage action, the flow process fluctuates up and down. Therefore, in this paper, the arithmetic moving-average algorithm (MA) is applied after the output neuron before the final model output to obtain the forecast flow. In the process of model training, the parameter nm needs to be adjusted based on experience.
From the perspective of the conventional hydrological forecasting model, the model developed in this paper is equivalent to a model that simulates the rainfall-runoff of the basin unit by unit, automatically calibrates and calculates the runoff depth with API and rainfall, then uses the unit hydrograph for confluence calculation, and finally adds the baseflow regression calculation. From the input layer to the first hidden layer of the ANN model, it is equivalent to calculate the runoff depth of a period by multiplying the API and the rainfall of the periods by different weights, which is also equivalent to the runoff depth calculation of the API model. From the first hidden layer to the second hidden layer, it is equivalent to the flow to the forecasting time calculated by multiplying the runoff depth concentration in each period by different weights, which is also equivalent to unit hydrograph calculation as shown by Hjelmfelt and Wang (1993).
The ANN model proposed in this paper, like the traditional API plus unit hydrograph model, uses the API, precipitation and initial river flow as the model inputs. Unlike traditional models, the ANN model has strong adaptability for automatic training and distributed rainfall-runoff processing. The ANN model automatically establishes the model through machine learning. After the model establishment, new rainfall and flood data can be input into the learning mechanism to automatic further train and optimize the model parameters. Results show that the ANN model developed in this paper achieved a satisfactory result. The rainfall-runoff calculation of the traditional API  plus unit hydrograph model in the three basins also has good accuracy; their runoff simulation error is about 5%, while the calculation of the runoff yield has not been improved. The most improvement of the ANN model is to facilitate the model calculation confluence. In many river basins, the existing traditional models have been used to produce multiple unit hydrographs for different types of floods. These existing unit hydrographs are applied for forecasting according to the location of rainstorm centre. Therefore, in operation forecasting the unit hydrograph is selected manually from those 3 to 11 different unit hydrographs in the traditional unit hydrograph forecasting models of the three watersheds based on experience. The ANN rainfall-runoff operational model developed in this paper can automatically operate, and be easy to use.
The model proposed in this paper takes the initial flow of the forecast river section as the input; it degenerates into regression calculation when there is no rainfall input. Therefore, the model proposed in this paper can also be used for the forecasting of base flow. The API and unit hydrograph models are widely used in flood forecasting, and the operational flood forecasting schemes are usually available for the development of this model in many rivers in China and other countries.

Conclusions
The ANN model proposed in this paper takes the key influencing factors according to the physical conceptions of rainfall-runoff formation, the initial Antecedent Precipitation Index (API), rainfall and upstream inflow and initial flow at the forecast river section as input, thus obtaining a model to simulate the whole process of a flood event. The distributed rainfall is realized as the input of the model, and the simulation is processed by dividing the watershed into several rainfall-runoff processing units. The model takes the data of the rainfall observation station as the input and adopts the training method of machine learning, which requires few data types. It realizes a flood forecasting model that is easy to use and practical to solve the problem of the heterogeneity of spatial distribution of rainfall, and is suitable for floods of different magnitude.
This model only connects the hidden layer neuron with the input which has physical conceptual causes, as the topological structure and the information transmission process are more consistent with the physical conception of rainfall-runoff. The model with a structure complying with physical conceptions achieves better results in real-time operational flood forecasting. In addition, the weight parameters of the model are reduced, so the distributed simulation of rainfallrunoff is easy to realize. The arithmetic moving-average algorithm is added to the output to simulate the pondage action of the watershed. The backpropagation (BP) training algorithm of MLP ANN is applied in this model.
Satisfactory results have been achieved in the study areas. The model proposed in this paper can use parameters of the widely accepted traditional hydrological models, which requires less data, is easy to practice in real-time operational forecasting and can be accepted by hydrologists in real-time flood forecasting.