APPLICATION OF ARTIFICIAL NEURAL NETWORKS FOR
RAINFALL-RUNOFF MODELLING
D. NAGESH KUMAR and ABHIJIT RAY
Department of Civil Engineering
Indian Institute of Technology
Kharagpur -721 302, India.
ABSTRACT
Rainfall-Runoff models are mostly empirical in nature demanding the knowledge of a large number of
catchment parameters. On the contrary Artificial Neural Networks (ANN) can be deployed in cases
where the available data is limited. The present work involves the development of an ANN model
using Backward Propagation algorithm. The hydrologic variables used were Rainfall, Soil Moisture,
Evaporation and Runoff of monsoon months for a specific period. Model 1 involved the training of the
ANN model with Rainfall values only, the output being the Runoff. Whereas, in Model 2 the training
set consisted of Rainfall, Soil Moisture and Evaporation values, Runoff being the desired output. Effect
of number of layers in the network is also studied. A comparison of the performance of the two models
is carried out. The model yielding the least error is recommended for simulating the Rainfall-Runoff
characteristics of the watershed. The ANN model is applied to Lekkur watershed in Tamilnadu for
which the hydrologic data were available for 9 years. With the developed ANN model Runoff values
were predicted and they compared well with the observed values.
INTRODUCTION
Neurons are nerve cells and neural networks are networks of these cells. The cerebral cortex of the brain
is an example of a natural neural network. Somehow, such a network of neurons thinks, learns, feels
and remembers. Many attempts had been made in the past to build models to study such neural
networks. There are two major types of models - biological and technological. In biological modelling
the goal is to study the structure and function of real brain in order to explain biological aspects such
as behaviour. In technological modelling the goal is to study brains in order to extract concepts to be
used in new computational methodologies. The latter viewpoint is taken by several investigators
working in the area of artificial neural networks and nurocomputers (Hecht-Nielsen, 1988)
The artificial neural network (ANN) approach differ from the traditional approaches in stochastic
hydrology in the sense that it belongs to a class of data-driven approaches as opposed to traditional
model driven approaches.
In this paper, a neural network computer program was developed to carry out Rainfall-Runoff
modelling of Lekkur catchment area in Tamilnadu. The neural network was developed using the
generalized delta rule for a semi-linear feed forward net with error back propagation. The program code
was written in C in UNIX environment. The neural network model was treated as a Black Box, as the
relationships between the physical components of the catchment were not to be fed. Model 1 involved
the training of the ANN model with Rainfall values only, the output being the Runoff. Whereas, in
Model 2 the training pairs consisted of Rainfall, Soil Moisture and Evaporation values, Runoff being
the desired output.
COMPUTATIONS IN ANN
The computational process associated with an ANN is as follows: An artificial neuron (AN) receives
its inputs from a number of other ANs or from the external world (Lippmann, 1987). A weighted sum
of these inputs constitutes the argument of an activation function. This activation function is assumed
to be nonlinear. Hard limiting threshold, i.e., either the step or signum function, and soft limiting
threshold, i.e. sigmoidal, are the three most often used forms of non-linearities. The resulting value of
the activation function is the output of the AN. This output is distributed along the weighted
connections to other ANs.
The components of an input pattern constitute the inputs to the node in layer i. The outputs of
the nodes in that layer may be taken to be equal to the inputs. The net input to a node in layer j is
netj = wkj oj
The output of node j is oj = f (netj), where f is the activation function. For a sigmoidal function we have
oj
1
1e
(net jj)/0
The parameter j serves as a threshold or bias and o is a constant to modify the shape of the sigmoidal
function (Yoh-Han Pao, 1985).
The semilinear feed forward net was proposed by Rumelhart et al.(1986). The back-propagation
training algorithm is an iterative gradient algorithm designed to minimize the mean square error between
the actual output of a multilayer feed-forward perceptron (Vemuri, 1988) and the desired output. It
requires continuous differentiable non-linearities (Lippmann, 1987). The steps involved are as follows,
STEP 1: Initialize Weights and Thresholds
Set all weights and thresholds to random numbers between - 0.5 to 0.5.
STEP 2: Present Inputs and Target Outputs
Present a continuous valued input vector x0 , x1,....., xN-1 and the corresponding t0, t1,....,
as the target or desired values.
tN-1
STEP 3: Calculate Actual Outputs
Use the sigmoidal non-linearity from above to calculate the outputs as oo, o1, ...., oN-1
STEP 4: Adopt Weights
Use a recursive algorithm starting at the output nodes and working back to the first hidden
layer. Adjust weights by
ûwji (n+1) = (/j oj) + . ûwji (n)
where is the momentum rate and . is acceleration. Also,
/k = (tk - ok) ok (1-ok)
where k denotes the output layer. And
/j = oj (1-oj) /k wkj
where j is any internal hidden layer.
STEP 5: Repeat by Going to Step 2.
Repeat the above steps till the conditions for iterations or error is satisfied.
RAINFALL-RUNOFF MODELS
Existing methods used to estimate runoff from rainfall are frequently classified into two groups viz.,
Black Box model and Process model (Todini, 1988). In the black box modelling approach, empirical
relations are used to relate runoff and rainfall, and only the input (rainfall) and the output (runoff) have
physical meanings. Simple mathematical equations, time-series methods and Neural networks methods
fall into this category. Process models attempt to simulate the hydrological processes in a catchments
and involve the use of many partial differential equations governing various physical processes and
equations of continuity for surface and soil water flow. Conceptual rainfall-runoff models (Chiew et.al.,
1993) can be considered as a third group of modelling approach.
NEURAL NETWORK APPLICATION
A rainfall-runoff model using ANNs for the Lekkur watershed in Tamilnadu state. The available
hydrologic parameters were Rainfall (mm), Soil Moisture (%), Evaporation (mm) and Runoff (mm)
values of the monsoon months (Jul-Sep) for 9 years (1975-83) (i.e. a total of 27 monthly data were
available). The raw data values of rainfall etc. were standardized by
zi
(xi x)/1n
where x and 1n are mean and standard deviation of the data. The zi values, which lie between -3.0 and
+3.0 were transformed between 0 and 1, and fed as the training set to the ANN.
The training parameter in Model 1 is only rainfall, whereas in case of Model 2 the training set
consists of rainfall, soil moisture and evaporation. For each model number of hidden layers are altered
i.e. Single hidden layer and Double hidden layer. The desired outputs from both the models is runoff.
Following parameters were kept constant for all the ANN models,
Momentum Rate
Acceleration
Permissible Average Absolute System Error
Permissible Mean Square System Error
Maximum Number of Iterations
=
=
=
=
=
0.9
0.7
0.012
0.0012
2,00,000
MODEL 1
Rainfall and runoff data of only 12 months were selected for training, as the dry spells yielded no runoff
data. These values were standardized, the rainfall values were fed in as the training input.
Single Hidden Layer
The ANN model consisted of a single hidden layer with 3 nodes in the hidden layer. As the number of
training cycles or iterations increased the system error decreased. After 2,00,000 iterations the training
data were fed in to the ANN model and the output values of the runoff were compared with the desired
or field observed data as shown in Fig. 1 . Final error in the model is,
Average Absolute System Error
Mean Square System Error
= 0.060784
= 0.003974
Double Hidden Layer
The model in this case consisted of a double hidden layer architecture, the hidden layers having 2 nodes
each. Fig. 2 shows the scatter plots between the output runoff values from the ANN, model and the field
observed data after 200,000 iterations. The errors obtained are as follows.
Average Absolute System Error
Mean Square System Error
= 0.047918
= 0.003158
MODEL 2
In model 2 the inputs for training were rainfall, soil moisture and evaporation values which were
standardized and transformed between 0 and 1. Two ANN models having different internal structures
i.e., one with single hidden layer and another with double hidden layer were studied. In each case the
model was trained with a set of 12 data points for a maximum of 200,000 training cycles. This was
followed by feeding the training set to the trained ANN model and the output thus obtained were
compared with the desired output values of runoff.
Single Hidden Layer
In this model the ANN had a single hidden layer with 3 nodes. A comparison of the output values with
the field observed data is given in Fig. 3. The errors obtained after 200,000 iterations are,
Average Absolute System Error
Mean Square System Error
= 0.012000
= 0.000194
Double Hidden Layer
In this case two hidden layered structure of the ANN model was adopted. Both the hidden layers
consisted of 2 nodes each. The comparison between the output values and the actual field observed data
is given in Fig. 4. The errors obtained after 200,000 iterations are,
Average Absolute System Error
Mean Square System Error
= 0.149618
= 0.092816
PREDICTION OF RUNOFF USING ANN MODEL
It can be clearly observed that the ANN model yielding the least error, both in terms of average absolute
error and mean square error, is model 2 having a single hidden layer. This model is then used for
predicting the runoff values for the next 4 consecutive rainfall months and the result is compared with
the actual observed field data. These predictions comapred well with the observed values as can be seen
from Table 1.
Table 1. Runoff predicton using ANN Model (Single hidden layer)
Rainfall
Soil moisture
Evaporation
Predicted runoff
Observed runoff
0.526
0.325
0.429
0.880816
0.622065
0.314
0.413
0.248
0.380117
0.271541
0.353
0.410
0.642
0.511718
0.435396
0.334
0.447
0.523
0.432945
0.246652
CONCLUSIONS
Artificial Neural Networks (ANN) are promising and show good capability to model the hydrologic
data. ANN with feed-forward network and backward propogtion algorithm is developed in the presetn
study. For the case study, ANN model with three input nodes and single hidden layer is found to be the
best for the rainfall-runoff modelling. ANN model's predictions comapred well with those observed.
Acknowledgements
The funds for this work are provided by DST under 'Scheme for Young Scientists' with project no.
HR/OY/O-02/97. The auhtors wish to acknowledge DST for providing funds.
REFERENCES
1
2
3
4
5
6
7
Hecht-Nielsen, R., 'Neurocomputing: Picking the human brain', IEEE Spectrum, 25(3), March 1988,
pp.36-41.
Vemuri, V., Edited., 'Artificial Neural Networks: Theoretical concepts', IEEE Computer society
Technology series, 1988, pp.145.
Yoh-Han Pao, 'Adaptive pattern recognition & Neural netowrks', Addison-Wesley Pub., 1985.
Rumelhart, D.E., G.E. Hinton and R.J. Williams, 'Learning internal representations by error
propagation', in D.E. Rumelhart and J.J. McClelland (Eds), Parallel distributed processing:
Expolorations in the microstructure of cognition, Vol. 1: Foundations, MIT Press, 1986.
Lippmann, R..P., 'An introduction to computing with Neural nets', IEEE ASSP Magagine, April
1987, pp. 4-22.
Todini, E., 'Rainfall-Runoff modelling - Past, Present and Future', J. Hydrology, Vol. 100, 1988, pp.
341-352.
Chiew, F.H.S., M.J. Stewardson and T.A. McMahon, 'Comparison of Rainfall-Runoff modelling
approaches', Vol. 147, 1993, pp. 1-36.