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JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 8 NO 2, DECEMBER, 2010


 

DEVELOPMENT OF RAINFALL-RUNOFF FORECAST MODEL

 

E.O. Oyebode

  Department of Computer Science and Engineering, and    

   K.O. Adekalu

Department of Agricultural Engineering, Obafemi Awolowo University, Ile Ife,

 and    

S.A. Akinboro

Department of Information and Communication Technology, Bells University of Technology, Ota, Nigeria

 

E-mail: kunlebest4u@yahoo.com                       

 

Abstract

This study developed a neurofuzzy-based rainfall-runoff forecast model for river basin and evaluated the performance of the model. This was with a view to capturing the behaviour of hydrological and meterological variables involved in rainfall-runoff process to improve forecast accuracy of rainfall-runoff.Three hydrological variables were used for model development. Also, a three-layered feedforward model was developed using the same input variables in comparison with the neurofuzzy-based model. The simulation was done using MATLAB® 7.0. The simulation results showed that neurofuzzy-based model has higher coefficient of determination (R2) and lower root mean square error (RMSE) over the three-layered feedforward model.This study concluded that the neurofuzzy-based model improved the forecast accuracy of the rainfall-runoff of Benin-Owena river basin better than three-layered feedforward model using the same hydrological conditions.

 

Keywords: rainfall-runoff, feedforward, neurofuzzy-based, river basin

 


Introduction

Rainfall-runoff forecast has attracted the attention of researchers because of the uncertain behaviour of the variables involved in the rainfall-runoff process. Forecast of rainfall-runoff involves analysis of the details of hydrological process which is nonlinear and contributions of the variables involved in the process. Soil usage, rainfall intensity, rainfall duration and rainfall distribution are among factors that determine the volume of runoff. How to accurately relate all the parameters that determine runoff requires a great deal (Smith and Marshall, 2009). These variables of runoff also vary from catchment to catchment thereby making model developed for one catchment area extremely unapplicable to the other. Different forecasting approaches have been applied in order to be able to capture the rainfall-runoff process and modeling rainfall-runoff have been based on different assumptions depending on the model (Nazemi et al., 2003). As a result of the nature of rainfall-runoff process, accuracy of forecast is still a challenge.

 

The work is divided into segment as follows: The Benin-Owena river basin development authority, the rainfall-runoff models, three-layered feedforward model, the neurofuzzy model, the performance evaluation of the model and result discussion.

 

The Benin-Owena River Basin Development Authority

In 1977, Nigeria was divided into eight hydrological areas and Benin-Owena River Basin Development Authority (BORDA) fell into hydrological area 6, named WESTERN LITTORAL. A number of rivers under the catchment area 6 include Siluko, Osse, Ogbesse, Ethiope, Ofosu, Ossiomo, Oluwa, Owena and Oye. A total of 24 hydrological stations  were established by the Benin-Owena River Basin Development Authority. The Benin-Owena River Basin Development Authority (BORDA) catchment area is shown in Fig. 1.0. The three hydrological stations selected for the model development were Ikpoba, Okhunwan and Owan stations.


 

Fig. 1: Hydrological map of  Benin-Owena Catchment Area

 
 

 


The Rainfall-Runoff Models

Many forecast techniques have been developed to model the rainfall-runoff process. A classification of all the rainfall-runoff approaches given by (Abot and Refsgad, 1996) is shown in Figure


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Conceptual rainfall-runoff model is among



the popular models for rainfall-runoff (Uhlenbrook et al., 1999). In conceptual models, the internal descriptions of the various subprocesses are modeled attempting to represent, in a simplified way, the known physical processes. The entire physical process in the hydrologic cycle is mathematically formulated in the conceptual models. Generally, they are composed of a large number of parameters. Conceptual rainfall-runoff models are conceptualizations of the known hydrological processes assumed to give rise to observed hydrographs. Conceptual rainfall-runoff models are based on description of mutually interrelated storages representing physical elements in a catchment most of which are defined by the moisture contents in the storages. The equations in such models are semi-empirical, but still holding some physical laws. Generally, the use of conceptual models are associated with numerous model parameters while the interaction of these parameters are highly complicated and the optimizations of the model parameters may be accomplished by trial-and-error procedure (Bates and Campbell, 2001).

 

In physically-based distributed models, hydrological processes are captured using differential equations that are distributed in space. Contrary to conceptual models, a physically-based model does not consider water flows in a catchment to take place in few storage units. Rather water flows and energy can be obtained directly from partial differential equations such as Saint Venant equations for overland and channel flow (Soulis et al., 2000 ; Singh, 1996). Such models are usually applicable to catchments with complex channel network, varying spatial distribution of land use, soil type and vegetation cover, with complex aquifer system below the soil surface etc. They expressed relationship between surface water, groundwater and unsaturated zone. Because of the natural orientation of rainfall-runoff process a great deal of uncertainty is entered to the modeling procedure as models were based on assumptions, which do not hold in the real process.

 

Many researchers in different areas of science and technology have used the black box technique such as artificial neural network (ANN) approach to solve problems in control, function approximation and pattern classification. Artificial Neural Network does not require the complex nature of the underlying process under consideration to be explicitly described in a mathematical form. Artificial Neural Network approach to problem solving may not be able to find global optimum in complex problems and high dimensional parameter spaces (De Vos and Rientjes, 2005). This suggests the need for further problem solving techniques.

 

Three-Layered Feedforward Model

Among various architectures of ANN, the feedforward model is the mostly used network architecture for handling hydrological problems. Multiple layers of neurons with nonlinear transfer functions allow the network to learn nonlinear and linear relationships between input and output vectors (Jang, 1997). In this study, three-layered feedforward model was developed and the backpropagation algorithm was used for training of the model. The backpropagation algorithm belongs to a category of supervised training algorithm. Training data patterns were fed sequentially into the input layer, and this information was propagated through the network. The resulting output predictions were compared with a corresponding desired or actual output and mean squared error were calculated over the entire dataset and the intermediate weights were adjusted using appropriate learning rule until the error has decayed sufficiently. The model architecture is shown in Figure 3.0. The three input variables were Gauge Height, Rainfall and Evaporation Rates.

                                                                        (1)

 

The above represents the input variables into the network. The transfer function sigmoid was then applied to the inputs using equation (2).

                      i = 1, 2,…,n                                    (2)

The transformed target outputs obtained from the network are:

                                                                      (3)

       While the actual outputs from the observed is represented in

           


                                                                              (4)

The network seeks to minimise the difference between the actual outputs and the network outputs using the mean square error in equation (5).

Text Box: Evaporation RatesText Box: RainfallText Box: Gauge Height


                                                (5)

 

                                   

 

 

 

 

 

 

 

 

 



Non-linear sigmoid function, tansig was used at the hidden layer while the output used linear function, purelin to generate a single output at the output layer. The model architecture adopted after varying different number of neurons at the hidden layer was (3:8:1). Levenberg Marquadt training function, trainlm and Bayesian Regularisation, training algorithms were used with the model architecture. The feedforward model that used the Levenberg Marquadt was FFN1 while the model that used Bayesian Regularisation was FFN2. During the backpropagation training, the model output was compared to the observed real values and the differences as error was redistributed back into the network for adjustment that took place through the weights being adjusted repeatedly until the error for the datasets were sufficiently minimized.

 

The neurofuzzy technique is among the blackbox models used in solving engineering problems. It is a data driven approach to modelling (Nayak et al., 2007). It is a combination of artificial neural network and fuzzy logic approach. The approach combines the benefits of neural networks as well as of fuzzy logic systems. This also reduces the limitations of the two systems as their features are combined. Features present in neural network and fuzzy logic include: distributed representation of knowledge, model-free estimation, ability to handle data with uncertainty and imprecision etc. However, fuzzy logic has tolerance for imprecision of data, while neural networks have tolerance for noisy data. A neural network’s learning capability provides a good way to adjust expert’s knowledge and it automatically generates additional fuzzy rules and functions to meet certain specifications. On the other hand, the fuzzy logic approach possibly enhances the generalisation capability of a neural network by providing more reliable output when extrapolation is needed beyond the limits of the training data.

 

One of the widely used models of neurofuzzy for mapping input or output data is the adaptive neurofuzzy inference system by (Jang et al., 1997). At the computational level, a neurofuzzy model can be seen as a layered structure (network). It is an adaptive network. Figure 4.0 shows the architecture of a neurofuzzy model.


                                                                                   

 

 

 

 


 

It ha

 

 


 

 

 

 

 

s nodes and directional links through which the nodes are connected. Then output is also dependent on the parameters relating to these nodes and the learning procedure specifies how these parameters should be modified to minimize a prescribed error measure. In order to show different adaptive capabilities, both circle and square nodes are used in adaptive network. The square node has parameters while the circular node does not have parameters. The parameter set of an adaptive network is the union of the parameter sets of each adaptive node and to achieve a desired input-output mapping, the parameters are updated according to given training datasets and gradient descent method.

Layer one: This is the input layer that takes in crisp value x as the input into the corresponding membership function in the next layer. Its output is defined as

i = 1,…,n                                                                  (6)                               

 

Layer two: The node in

 

 

 

 

this layer, membership layer receives as input x1,…,xn and seeks similarity using the input values x1,…,xn and membership function. Units in the layer are arranged into groups that is G groups for each fuzzy rule. Each unit miG ϵ L2 receives xi and obtained miG(xi)  which stands for the degree to which the input value xi belongs to the fuzzy set  The output of this unit miG ϵ L2 can be obtained using equation (7)

i = 1,…,n

g =1,…,G

 
                                                                                (7)   

where cig and aig are respectively the mean and the width of the gausian membership function miG(.).

Layer three: the activation level of each rule formed in layer two is performed. The units are fixed and are usually equal to number G fuzzy rules. Output of unit ug ϵ L3 is computed using the rule activation strength defined in equation (8)

                                                                        (8)

Layer four: the fourth layer L4 is the defuzzification layer which results to output values. The output of unit uh ϵ L4 can be obtained using equation (9)

                   h = 1,…,m                                     (9)

 

The Neurofuzzy Model

Implementing neurofuzzy model can be done using two techniques which are grid-based partitioning and clustering technique. The grid-based fuzzy rule learning generates a partition or grid of the input and output spaces prior to creating the rule-based. The rules are obtained by selecting the adequate input and output labels according to the numerical data. However, based on previous work, accuracy of results obtained were not as good as those ones obtained with clustering even when network pruning was done (Paiva, 1999).

 

In this work, subtractive clustering was applied to group data points into classes or clusters so that members of the same cluster are more similar to each other in some sense than to members of other clusters (Jain and Chalisgaonkar, 2000). Clustering is useful for exploring the underlying structure of a given dataset and has been widely used in many scientific and engineering fields such as pattern recognition, image processing, data mining, etc. Subtractive clustering is based on a measure of the density of data points in the feature space (Chiu, 1994). The idea is to find regions in the feature space with high densities of data points. The point with the highest number of neighbours was selected as centre for a cluster. The data points within a prespecified fuzzy radius were then removed (subtracted), and the algorithm looks for a new point with the highest number of neighbours. This continued until all data points were examined. Initially, each data point was considered as a potential cluster centre. Then the density measure at data point Uk  can be defined  using equation ( 10)

                                                               (10)

 

where the positive constant ra  is the radius defining a neighbourhood of a cluster center. In this study radius of clustering was put as 0.2 and 0.4 in order to obtain fuzzy rules.

The model that used radius of clustering for the input dataset was NF1 and the model that used NF2 as 0.4 was NF2. Density measure for each data point was detected  and the point with the highest measure of density was selected as a first cluster centre. Other points were revised using equation (11).

                                                          (11)

 


rb was determined by the model as value a little higher than ra. For the training of the models, Ikpoba gauging station dataset was used for the training, Owan station for validation and Okhunwan dataset for the testing of the models. Fuzzy Inference System that contained the rules that mapped the input space to the output space was generated using the three input variables. fig shows the degree of membership of the input 


variable and the fuzzy inference system for the input variables is shown in Figure 5.0


 

Text Box: Degree of membership 

 

 

 

 


Text Box:

Figure 6: Fuzzy Inference System

 

Figure 6.0:Fuzzy inference system

 
 

 

 

 

 

 

 




Table 1: Dataset  for Model Development

                                              Owan Station

 

 

Statistical parameter

Gauge Height

Water Discharge

Rainfall

Evaporation Rates

Runoff

 

 

 

 

 

 

Min

0.001

0.010

0.000

1.100

53000000

Max

5.960

17.900

133.400

11.900

626000000

Mean

1.833

3.119

1.619

3.163

122680540

Standard Dev

1.766

3.119

10.998

2.185

99618966

                                             Okhunwan Station

 

 

 

Statistical parameter

 

Gauge Height

 

Water Discharge

 

Rainfall

 

Evaporation Rates

 

Runoff

 

 

 

 

 

 

Min

1.680

1.700

0.000

1.200

71000000

Max

46.000

57.200

10.670

11.000

168000000

Mean

17.260

24.508

0.762

2.645

109651376

Standard Dev

16.931

20.204

1.601

1.679

29522803

                                                 Ikpoba Station

 

 

Statistical parameter

Gauge Height

Water Discharge

Rainfall

Evaporation Rates

Runoff

 

 

 

 

 

 

Min

1.110

4.780

0.000

1.000

18000000

Max

4.150

65.400

1.561

6.210

626000000

Mean

2.402

28.761

0.055

2.585

86575653

Standard Dev.

.724

28.761

0.138

1.147

86227309

 

  Source:Benin-Owena River Basin Development Authority (BORDA)

 


Performance Evaluation of the Model

For the purpose of evaluating the model, coefficient of determination and root mean square error were chosen as performance statistics with which the model can be assessed in terms of accuracy. The neurofuzzy-based and three-layered feedforward network models were subjected to the same conditions and  the performance evaluation statistics, coefficient of determination, R2 and root mean square error  were used to determine the accuracy.

                                                                                                                                                  

Coefficient of determination,

 
 


(14)

 

 

                       

Correlation coefficient, cc

 

Root mean square error, RMSE

 

 

 

 


 
                                                                                                                                                      (15)  

 

 

Where n is the number of observations, Qobs and Qcal are the observed and calculated values, and Q av, Qcal-av are the mean of the observed and calculated values respectively.

 

Result Discussion

The model forecast results did not show significant difference between the model predictions and observed. During the training of the models, the neurofuzzy-based models have highest coefficient of determination, R2 and least mean square error as shown in table 2.0. The graphs of the neurofuzzy-based models were shown in Figure 7.0 and Figure 7.1 while the graphs of the three-layered feedforward network were shown in Figure 7.2 and Figure 7.3 respectively.

 

During the model testing, the three-layered feedforward model, FFN2 with Bayesian Regularisation function as training produced the least coefficient of determination, R2 = 0.983 and highest root mean square error, RMSE = 1.572 while the neurofuzzy-based model with radius of clustering = 0.2 gave the highest coefficient of determination, R2 = 0.990 and least root mean square error, RMSE = 1.076 as shown in table 3.0. The graphs of the neurofuzzy-based models were shown in Figure 7.4 and Figure 7.5 while the graphs of the three-layered feedforward network were shown in Figure 7.6 and Figure 7.7 respectively.

 

Using the statistical indices obtained during training and testing of the models, the neurofuzzy-based models demonstrated higher accuracy than the three-layered feedforward network models. The three-layered feedforward model that used Levenberg Marquadt, trainlm also showed improved accuracy over Bayesian Regularisation, trainbr in this study.

 

This research effort is relevant to determine the rainfall-runoff forecast of the tropical region as the case study selected for the work fell into tropical region. The results from the study is important to the hydrologists in determining the rainfall-runoff pattern of the tropical region. The results can further be used with some models like Autoregressive Moving Average model in order to determine the long term forecast of rainfall-runoff in the tropical region. Such accurate forecast is important in managing hydrological structures located around the Benin-Owena River Basin Development Authority to increase the life span of such structures which can also turnout to safe costs.

 


Table 2.0:Performance Statistical Table for Training Result

Model Type

Neurofuzzy

FeedForward Network

Model Identification

NF1

NF2

FFN1

FFN2

Coefficient of Determination, R2

0.982

0.973

0.966

0.964

Root Mean Square Error, RMSE

1.125

1.230

1.590

2.650

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Table 3.0:Performance Statistical Table for Testing Result

Model Type

Neurofuzzy

Feed Forward Network

Model Identification

NF1

NF2

FFN1

FFN2

Coefficient of Determination, R2

0.990

0.986

0.985

0.983

Root Mean Square Error, RMSE

1.076

1.220

1.450

1.572

 

Figure 7.4: NF1 (Neurofuzzy) Model Graph Using Okhunwan

                  Station

 

 

Figure 7.6: FFN1 (ANN) Model Result Using Okhunwan

   Station

 
 

 




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