JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 8 NO 2, DECEMBER, 2010
DEVELOPMENT OF RAINFALLRUNOFF 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
Email:
kunlebest4u@yahoo.com
Abstract
This study developed a neurofuzzybased rainfallrunoff 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
rainfallrunoff process to improve forecast accuracy of rainfallrunoff.Three
hydrological variables were used for model development. Also, a threelayered
feedforward model was developed using the same input variables in comparison
with the neurofuzzybased model. The simulation was done using MATLAB^{®}
7.0. The simulation results showed that neurofuzzybased model has higher
coefficient of determination (R^{2}) and lower root mean square error
(RMSE) over the threelayered feedforward model.This study concluded that the
neurofuzzybased model improved the forecast accuracy of the rainfallrunoff of
BeninOwena river basin better than threelayered feedforward model using the
same hydrological conditions.
Keywords: rainfallrunoff, feedforward, neurofuzzybased, river basin
Introduction
Rainfallrunoff forecast has attracted the attention of researchers because of
the uncertain behaviour of the variables involved in the rainfallrunoff
process. Forecast of rainfallrunoff 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 rainfallrunoff process and modeling
rainfallrunoff have been based on different assumptions depending on the model
(Nazemi et al., 2003). As a result of
the nature of rainfallrunoff process, accuracy of forecast is still a
challenge.
The work is divided into segment as follows: The BeninOwena river basin
development authority, the rainfallrunoff models, threelayered feedforward
model, the neurofuzzy model, the performance evaluation of the model and result
discussion.
The BeninOwena River Basin Development Authority
In 1977, Nigeria was divided into eight hydrological areas and BeninOwena 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 BeninOwena River Basin Development Authority. The
BeninOwena 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.

The RainfallRunoff Models
Many forecast techniques have been developed to model the rainfallrunoff
process. A classification of all the rainfallrunoff approaches given by (Abot
and Refsgad, 1996) is shown in Figure
Conceptual rainfallrunoff model is among
the popular models for rainfallrunoff (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
rainfallrunoff models are conceptualizations of the known hydrological
processes assumed to give rise to observed hydrographs. Conceptual
rainfallrunoff 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
semiempirical, 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 trialanderror procedure (Bates and
Campbell, 2001).
In physicallybased distributed models, hydrological processes are captured
using differential equations that are distributed in space. Contrary to
conceptual models, a physicallybased 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 rainfallrunoff 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.
ThreeLayered 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, threelayered 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).
(5)
Nonlinear 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, modelfree 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 inputoutput 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 x_{1},…,x_{n} and
seeks similarity using the input values x_{1},…,x_{n} and
membership function. Units in the layer are arranged into groups that is G
groups for each fuzzy rule. Each unit
m_{iG}
ϵ L_{2 }receives x_{i }and obtained
m_{iG}(x_{i}) which stands for the degree to which
the input value x_{i }belongs to the fuzzy set
The output of this unit
m_{iG}
ϵ L_{2} can be obtained using equation (7)

where c_{ig }and a_{ig} are respectively the mean and the width
of the gausian membership function
m_{iG}(.).
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 u_{g}
ϵ L_{3} is computed using the rule activation strength defined in
equation (8)
(8)
Layer four:
the fourth layer L_{4} is the defuzzification layer which results to
output values. The output of unit u_{h} ϵ L_{4} can be obtained
using equation (9)
h = 1,…,m
(9)
The Neurofuzzy Model
Implementing neurofuzzy model can be done using two techniques which are
gridbased partitioning and clustering technique. The gridbased fuzzy rule
learning generates a partition or grid of the input and output spaces prior to
creating the rulebased. 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
U_{k } can be defined using equation ( 10)
(10)
where the positive constant r_{a } 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)
r_{b} was determined by the model
as value a little higher than r_{a}. 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



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:BeninOwena 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 neurofuzzybased and threelayered
feedforward network models were subjected to the same conditions and the performance evaluation
statistics, coefficient of determination, R^{2} and root mean square
error were used to determine the
accuracy.

(14)



Where n is the number of observations, Q_{obs }and_{ }^{Q}_{cal
}are the observed and calculated values, and Q_{ av}, Q_{calav}
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
neurofuzzybased models have highest coefficient of determination, R^{2}
and least mean square error as shown in table 2.0. The graphs of the
neurofuzzybased models were shown in Figure 7.0 and Figure 7.1 while the graphs
of the threelayered feedforward network were shown in Figure 7.2 and Figure 7.3
respectively.
During the model testing, the threelayered feedforward model, FFN2 with
Bayesian Regularisation function as training produced the least coefficient of
determination, R^{2 }= 0.983 and highest root mean square error, RMSE =
1.572 while the neurofuzzybased model with radius of clustering = 0.2 gave the
highest coefficient of determination, R^{2 }= 0.990 and least root mean
square error, RMSE = 1.076 as shown in table 3.0. The graphs of the
neurofuzzybased models were shown in Figure 7.4 and Figure 7.5 while the graphs
of the threelayered 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 neurofuzzybased models demonstrated higher accuracy than the
threelayered feedforward network models. The threelayered 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 rainfallrunoff 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 rainfallrunoff 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 rainfallrunoff in the tropical
region. Such accurate forecast is important in managing hydrological structures
located around the BeninOwena 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, R^{2} 
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, R^{2} 
0.990 
0.986 
0.985 
0.983 
Root Mean Square Error, RMSE 
1.076 
1.220 
1.450 
1.572 




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