Estimation or forecasting the magnitude of hydrological variables is required in case of extreme events risk management, water resources planning and management and river structures operation. Flood warning, drought forecasting and optimal operation of the reservoirs and power plants can be performed by appropriate river flow forecasting.
Many approaches have been used to hydrologic forecasting in the last few decades. These models are grouped into three categorizes (Babovic and Bojkow, 2001).
Lumped conceptual models: These types of models approximate the general internal sub-processes and physical mechanisms which govern the hydrologic cycle. The implementation and calibration of lumped conceptual models is encountered with some difficulties, requires significant amount of calibration data and depends on the expertise and experience of the user.
Distributed physically based models: There are not so many models of this kind, suitable for research. This type of modeling systems needs a large amount of data. They utilize many parameters in their operation in a direct relation to topology, soil, vegetation and geology characteristics of catchments. In the other hand, many of these parameters are not directly measured everywhere in the studied basin.
Empirical black box models: These kinds of models do not use any explicit well-defined representation of the physical process and governing equations of the phenomena. The accuracy of these models is highly dependent on the quality of the observed data used to calibrate or train them. However, it has been shown that these models are useful operational tools and they are the only option in case where there are not enough meteorological data available.
In this regard, Artificial Neural Networks are non-linear, distributed, heuristic and adaptive learning models constructed from many simple processing elements, called Neuron.
Artificial Neural Network (ANN) is a mathematical tool, which tries to represent low-level intelligence in natural organisms (Gorzalczany, 2002) and it is a flexible structure, capable of making a non-linear mapping between input and output spaces.
Neural network processing is based on performance of many simple processing
units called neuron. Each neuron in each layer is connected to all elements
in the previous and the next layer with links, each has an associative weight.
The general ability of an ANN is to learn (Karayiannis and Venetsanopoulos,
1993) and to simulate the natural and complex phenomena.
The application of the ANN in hydrology, especially in rainfall-runoff modeling, has become very popular in recent years. The particular advantage of ANN is that, even if the exact relationship between sets of input and output data are unknown but is acknowledged to exist, the network can be trained to learn that relationship, requiring no a prior knowledge of the watershed characteristics (Pang et al., 2007). Such applications can be found in many papers published recently (French et al., 1992; Zhu et al., 1994; Hsu et al., 1995; Smith and Eli, 1995; Minns and Hall, 1996; Shamseldin, 1997; Campolo et al., 1999; Gautam et al., 2000; Imrie et al., 2000; Chang and Chen, 2001; Shamseldin and OConnor, 2001; Xiong and OConnor, 2002; Sivakumar et al., 2002; Campolo et al., 2003; Wilby et al., 2003; Jain et al., 2004; Rajurka et al., 2004; Xiong et al., 2004; Chau et al., 2005; Chau, 2006; Dawson et al., 2006). From all these works, ANN models can be divided into updating mode and simulation mode. When the network input includes the runoff or the water level for the previous time period, such ANN models are in updating mode. It is the most popular mode of recent ANN applications and applied with varying degrees of success. Shamseldin (1997) and Rajurka et al. (2004) have developed the ANN models with simulation mode. Comparing with other empirical black-box models, the ANN models of simulating mode also show advantages in flood simulation and forecasting. According to the two modes, The ANN models are regarded as black-box models that cannot provide any physically realistic structure and parameters to represent the hydrological processes in watersheds, even though they are capable of identifying complex nonlinear relationships between rainfall and runoff time series. Hsu et al. (1995) have showed that the ANN approach does provide a viable and effective alternative to the ARMAX time series approach for developing input-output simulation and forecasting models in situations that do not require modeling of the internal structure of the watershed.
MATERIALS AND METHODS
Case study and dataset: The aim of this study is to predict the hourly
discharge (in 12 h steps) for Kashkan River at Poledokhtar hydrometry station,
located in the Karkheh River Basin in the South-West of Iran which is showed
in Fig. 1. Multi Layer Perceptron (MLP) and Radial Basis Function
(RBF) neural networks are used and compared to the NAM hydrologic model which
utilizes a Shuffled Complex Evolution (SCE) algorithm for model automatic calibration.
||Kashkan River sub-basin
In this regard, discharges at Poledokhtar station, precipitation, evaporation
and temperature of 11 different stations during the period of 1994-1999 have
been collected, in which the greatest floods occurred and divided into two sets
for model training/calibration and verification. The training/calibration set
is the data from the period of 1994-1998 and the rest of data is used to verification.
Multi layer perceptron: The MLP network, sometimes called Back Propagation (BP) network, is shown in Fig. 2, is probably the most popular ANN in engineering problems in the case of non-linear mapping and is called Universal Approximator (Hecht-Nielson, 1987).
The learning process is performed using the well-known BP algorithm (Werbos, 1974; Rumelhart et al., 1986). In this study, the standard BP algorithm based on the delta learning rule is used.
Two main processes are performed in a BP algorithm. A forward pass and a backward pass. In the forward pass, an output pattern is presented to the network and its effect is propagated through the network, layer by layer. For each neuron, the input value is calculated as follows:
||The input value of ith neuron in nth
||The connection weight between ith neuron in nth
layer and jth neuron in the (n-1)th layer
||The output of jth neuron in the (n-1)th layer
||The No. of neurons in the (n-1)th layer
In each neuron, the value calculated from Eq. 1 is transferred by an activation function. The common function for this purpose is the sigmoid function, which is given by:
Hence, the output of each neuron is computed and propagated through the next layer until the last layer. Finally, the computed output of the network is prepared to be compared with the target output. In this regard, an appropriate objective function such as the Mean Relative Error (MRE) or Root Mean Square Error (RMSE) is calculated. The former which is used in this study is computed as follows:
||The jth element of the target output vector related to the
||The computed output of jth neuron related to the pth
||The number of patterns
||The number of neurons in the output layer
After calculating the objective function, the second step of the BP algorithm, i.e., the backward process is started by back propagation of the network error to the previous layers. Using the gradient descent technique, the weights are adjusted to reduce the network error by performing the following equation (Rumelhart et al., 1986):
||The weight increment at the (m+1)th iteration (Epoch)
||The learning rate
||The momentum term, both in the range of (0, 1) (Rumelhart et al.,
This process is continued until the allowable network error is occurred.
Radial basis function neural network: The RBF network is a feed forward network consists of one hidden layer. The activation function of the hidden layer is often a Gaussian function and the output layer has often linear functions (Dibike et al., 1999; Mason et al., 1996). Learning of a RBF network is generally divided into two phases. The first one is an unsupervised (self-organizing) in which the hidden unit parameters depend on the input distribution are adjusted. The second one is a supervised learning in which the weights between hidden and linear output layer are adjusted using gradient descent or linear regression techniques.
A RBF hidden neuron has one parameter associate with each input neuron. These parameters, wij, are the centers of units. The output of each hidden neuron is a function of the distance between the input vector X = (x1, x2,
, xn) and radial center vector Wj = (w1j, w2j,
, wnj) and can be written as follows:
The hidden neuron output can be calculated in many ways. The most popular activation function for this purpose is the Gaussian one described as follows (Mason et al., 1996):
where, λ is a constant. At last the output layer computes the output as follows:
||The weight coefficient between jth neuron between hidden layer
and kth neuron of output layer
|| The output of the jth hidden neuron
ANN modeling assumptions: The performance of rainfall-runoff black box modeling is highly dependent on the type and number of input elements. In this regard, several models indicating different number of input elements are evaluated as follows:
M1: Q (t) = f [Pi (t)], i = 1, 2,....,11
M2: Q (t) = f [Q (t-1), Q (t-2)],
M3: Q (t) = f [Q (t-1)], Pi(t)] i = 1, 2,....,11
||The precipitation at ith station at the tth time
Many researchers have reported the importance of careful data preparation and the choice of effective input variables (Dawson and Wilby, 1998). So, the aforementioned three models (M1,
, M3) are evaluated using the MLP and RBF neural networks.
Lumped conceptual rainfall-runoff model: The basis and general concepts that govern this model is based on the NAM (Nedbør Affstrømnings Model) model (Nielsen and Hansen, 1973). In this model, the quantitative simulation of watershed is based on hydrologic cycle and its parameters represent an average value for the whole watershed. Figure 3 shows the general structure of the model with its four different and mutually interrelated storages and their corresponding flows. The four storage layers are snow storage, surface storage, lower zone storage and underground storage and the three flows are surface flow (QOF), interflow (QIF) and underground flow (QBF). Generally, the input data needed for this model are rainfall, potential evaporation and temperature and the output of the model is the watershed outflow with respect to time.
In this study, Shuffled Complex Evolution (SCE) methodology is implemented as the NAM automatic calibration tool. To obtain the global optimization point, this method uses four basic concepts. These concepts are combination of random and deterministic approaches, clustering, the concept of a systematic evolution of a complex of point spanning the space, the concept of competitive evolution (Holland, 1975). The success of each of the above concepts in separate applications has been proved (Sorooshian et al., 1993; Duan et al., 1992; Holland, 1975; Wang, 1991). The combination of these concepts made the SCE known as a powerful, effective and flexible method. A detailed application of SCE in NAM model auto calibration for Karkheh River Basin in west of Iran is reported by Eslami et al. (2005). A general description of the steps of the SCE-UA method is given below (Duan et al., 1994):
||Schematic structure of the NAM model
Step 1: Generate sample: Sample s points randomly in the feasible parameter space and compute the criterion value at each point. In the absence of prior information on the approximate location of the global optimum, use a uniform probability distribution to generate a sample.
Step 2: Rank points: Sort the s points in order of increasing criterion value so that the first point represents the smallest criterion value and the last point represents the largest criterion value (assuming that the goal is to minimize the criterion value).
Step 3: Partition into complexes: Partition the s points into p complexes, each containing m points. The complexes are partitioned such that the first complex contains every p (k-1) + 1 ranked point, the second complex contains every p (k-1) + 2 ranked point and so on, where, k = 1, 2,. . . . . m.
Step 4: Evolve each complex: Evolve each complex according to the Competitive Complex Evolution (CCE) algorithm (which is elaborated below).
Step 5: Shuffle complexes: Combine the points in the evolved complexes into a single sample population; sort the sample population in order of increasing criterion value; shuffle (i.e., re-partition) the sample population into p complexes according to the procedure specified in Step 3.
Step 6: Check convergence: If any of the pre-specified convergence criteria are satisfied, stop; otherwise, continue.
Step 7: Check the reduction in the number of complexes: If the minimum number of complexes required in the population, pmin, is less than p, remove the complex with the lowest ranked points; set p = p-1 and s = pm; return to Step 4. If pmin = p, return to Step 4.
The initial random sampling of the parameter space provides the potential for locating the global optimum without being biased by pre-specified starting points. The partition of the population into several communities facilitates a freer and more extensive exploration of the feasible space in different directions, thereby allowing for the possibility that the problem has more than one region of attraction. The shuffling of communities enhances the survivability by a sharing of the information (about the search space) gained independently by each community. One key component of the SCE-UA method is the CCE algorithm, as mentioned in Step 4. This algorithm is based on the Nelder and Mead (1965) Simplex downhill search scheme.
RESULTS AND DISCUSSION
The training/calibration and verification datasets described in the previous sections are used to learn/calibrate and test the ANNs and NAM models. Many different architectures, including number of hidden layers for the MLP, number of hidden neurons for both MLP and RBF, activation functions for the MLP and number of optimal epochs For the MLP are evaluated during the training and verification phases.
The model performance is evaluated using Mean Relative Error (MRE) and Nash-Sutcliffe between the observed and forecasted discharges. The former function is recommended in case of flood forecasting (Nash and Sutcliffe, 1970) which is computed as follows:
|Qo and Qp
||Observed and predicted discharge at time t, respectively
||Denotes the mean observed discharge
The results are shown in Table 1. As shown in Table 1, the performance of the MLP neural network is generally better than other models for Kashkan River Basin with available data. On the other hand, when antecedent discharges were added to the input pattern, the performance of the ANNs is improved.
Comparing both applied neural networks indicate that the RBF performance is superior to the MLP, when precipitation is the only input parameter (M1 model), whereas river flow forecasting without exogenous inputs (M2 model) is better performed using the MLP neural network. On the other hand, both MLP and RBF neural network forecasts, improved when M3 modeling assumption is mentioned. Comparing applied neural networks to the NAM model shows that the MLP network trained with M3 modeling assumption is the most superior model in both training/calibration and verification periods.
Forecasted discharges by proposed MLP (trained through M3 modeling assumption) and the NAM model, versus observed discharge is plotted for the training/calibration and verification datasets in Fig. 4 and 5, respectively.
Figure 6 and 7 show the observed and forecasted
hydrographs by proposed MLP and the NAM models in the verification period.
Integration of plotted points near the line y = x in Fig. 5 and 6 clearly indicates the superiority of the MLP neural network performance in these graphs. In detail, low and high flows are forecasted adequately by the MLP compared to the NAM model.
As Fig. 6 and 7 show, it can be obviously
seen that both base flow and peak discharges are more precisely predicted by
the MLP neural network. Returning to the Table 1 indicates
the effective role of antecedent discharge in the improvement of the MLP forecasts.
||Performance evaluation of different models
||Forecasted versus observed discharge in the training/calibration
||Forecasted versus observed discharge in the verification period
||Observed and forecasted hydrographs in the verification period
||Observed and forecasted hydrographs in the verification period
Artificial Neural Networks can provide useful tools in analyzing and solving a wide range of problems of water engineering in a simpler structure and faster training rather than conceptual models. ANNs are robust and flexible tools, trained by example illustration and act as a distributed memory to save the inner knowledge of training data.
Multi Layer Perceptron neural network applied to Kashkan River flow forecasting shows encouraging performance compared to Radial Basis Function neural network and NAM hydrologic model with SCE algorithm for auto calibration in case of peak flood and base flow forecasting. Comparing both applied neural networks in Kashkan river flow forecasting indicate that the RBF performance is slightly superior to the MLP, when precipitation is the only input parameter (M1 model), whereas river flow forecasting without exogenous inputs (M2 model) is better performed using the MLP neural network.
Furthermore, it is concluded that the presence of the discharge in the previous time step as model input can greatly improve the ANN forecasts.
The authors would like to express their gratitude to Water Research Institute for their support and consent.