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DEVELOPMENT OF RAINFALL – RUNOFF MODEL USING
ARTIFICIAL NEURAL NETWORK FOR A PRIYADARSHINI
WATERSHED
A Thesis submitted to the
Dr. BALASAHEB SAWANT KONKAN KRISHI VIDYAPEETH
DAPOLI - 415 712
Maharashtra State (India)
In the partial fulfillment of the requirements for the degree
of
MASTER OF TECHNOLOGY
(AGRICULTURAL ENGINEERING) in
SOIL AND WATER CONSERVATION ENGINEERING
by
KOTHE SWAPNIL AJAY
B. Tech (Agril. Engg.)
DEPARTMENT OF SOIL AND WATER CONSERVATION ENGINEERING
COLLEGE OF AGRICULTURAL ENGINEERING AND TECHNOLOGY
DR. BALASAHEB SAWANT KONKAN KRISHI VIDYAPEETH
DAPOLI- 415 712, DIST. RATNAGIRI, M. S. (INDIA)
2015
ii
iii
CANDIDATE‟S DECLARATION
I hereby declare that this thesis or part thereof has not been submitted
by me or any other person to any other
University or Institute
for a Degree or
Diploma.
Place: CAET, Dapoli (Swapnil Ajay Kothe)
Dated: / /2015
iv
Dr. B. L. Ayare
B. Tech. (Agril. Engg.), M. Tech. (WRDM), Ph.D (SWCE)
Agricultural Engineer,
AICRP on Water Management, Wakawali,
Dr. Balasaheb Sawant Konkan Krishi Vidyapeeth, Dapoli – 415 712
Dist. Ratnagiri, Maharashtra State (India).
CERTIFICATE
This is to certify that the thesis entitled “DEVELOPMENT OF RAINFALL–
RUNOFF MODEL USING ARTIFICIAL NEURAL NETWORK MODEL FOR A
PRIYADARSHINI WATERSHED”, submitted to Faculty of Agricultural Engineering, Dr.
Balasaheb Sawant Konkan Krishi Vidyapeeth, Dapoli, Dist. Ratnagiri (Maharashtra State) in
partial fulfillment of the requirements for the award of the degree of Master of Technology
(Agricultural Engineering) in Soil and Water Conservation Engineering, embodies the
record of a piece of bonafied research work carried out by Mr. Swapnil Ajay Kothe under
my guidance and supervision. No part of this thesis has been submitted for any other degree,
diploma or publication in any other form.
The assistance and help received during the course of this investigation and source of
the literature have been duly acknowledged.
Place : CAET, Dapoli (B. L. Ayare)
Date : / / 2015
v
Prof. dilip MAHALE
B. Tech. (Agril. Engg.), M. Tech. (SWCE)
Professor and Head,
Department of Soil and Water Conservation Engineering,
College of Agricultural Engineering and Technology,
Dr. Balasaheb Sawant Konkan Krishi Vidyapeeth, Dapoli – 415 712
Dist. Ratnagiri, Maharashtra State (India).
CERTIFICATE
This is to certify that the thesis entitled “DEVELOPMENT OF RAINFALL–
RUNOFF MODEL USING ARTIFICIAL NEURAL NETWORK MODEL FOR A
PRIYADARSHINI WATERSHED”, submitted to Faculty of Agricultural Engineering, Dr.
Balasaheb Sawant Konkan Krishi Vidyapeeth, Dapoli, Dist. Ratnagiri (Maharashtra State) in
partial fulfillment of the requirements for the award of the degree of Master of Technology
(Agricultural Engineering) in Soil and Water Conservation Engineering, embodies the
record of a piece of bonafied research work carried out by Mr. Swapnil Ajay Kothe under
the guidance and supervision of Dr. B. L. Ayare, Agricultural Engineer, AICRP on Water
Management, Wakawali, Dr. Balasaheb Sawant Konkan Krishi Vidyapeeth, Dapoli. No part
of the thesis has been submitted for any other degree, diploma or publication in any other
form.
The assistance and help received during the course of this investigation and source of
the literature have been duly acknowledged.
Place : CAET, Dapoli (dilip MAHALE)
Date : / / 2015
vi
Dr. N. J. Thakor
B.Tech (Agril. Engg.), M. Tech (IIT), Ph.D (Canada), FIE, FISAE
Associate Dean,
College of Agricultural Engineering and Technology,
Dr. Balasaheb Sawant Konkan Krishi Vidyapeeth, Dapoli – 415712.
Dist. Ratnagiri, Maharashtra State (India).
CERTIFICATE
This is to certify that the thesis entitled “DEVELOPMENT OF RAINFALL-
RUNOFF MODEL USING ARTIFICIAL NEURAL NETWORK MODEL FOR A
PRIYADARSHINI WATERSHED”, submitted to Faculty of Agricultural Engineering, Dr.
Balasaheb Sawant Konkan Krishi Vidyapeeth, Dapoli, Dist. Ratnagiri (Maharashtra State) in
partial fulfillment of the requirements for the award of the degree of Master of Technology
(Agricultural Engineering) in Soil and Water Conservation Engineering, embodies the
record of a piece of bonafied research work carried out by Mr. Swapnil Ajay Kothe under
the guidance and supervision of Dr. B. L. Ayare, Agricultural Engineer, AICRP on Water
Management, Wakawali, Dr. Balasaheb Sawant Konkan Krishi Vidyapeeth, Dapoli. No part
of the thesis has been submitted for any other degree, diploma or publication in any other
form.
The assistance and help received during the course of this investigation and source
of the literature have been duly acknowledged.
Place : CAET, Dapoli (N. J. Thakor)
Dated : / / 2015
vii
ACKNOWLEDGEMENT
„The programmatic approach to problem must play a certain role in development
initiatives‟. My guide who made us to realize this thing, Dr. B. L. Ayare, Agricultural
Engineer, AICRP on Water Management, Wakawali, Dr. Balasaheb Sawant Konkan Krishi
Vidyapeeth, Dapoli assisted me to construct every stepping-stone leading towards this project
success. I seize this opportunity to express my frequent puissant and scholastic guidance,
immutable interest, constructive criticism and timely help.
I feel deep sense of gratitude to express my heartful thanks to Dr. N. J. Thakor,
Associate Dean, Faculty of Agricultural Engineering and Technology, Dr.B.S.K.K.V., Dapoli,
for his rewarding guidance and kind help in providing necessary facility in time made the
research study and achievement.
I am also highly obliged to Prof. dilip. MAHALE, Professor and Head, Department
of Soil and Water Conservation Engineering, College of Agricultural Engineering and
Technology, Dapoli for his valuable guidance, timely suggestion and constant
encouragement.
I am equally indebted to, Dr. S. B. Nandgude, Associate Professor, and Prof. H. N.
Bhange, Assistant Professor, Department of Soil and Water Conservation Engineering,
College of Agricultural Engineering and Technology, Dapoli for arousing our interest and
amending the work timely.
I am also indebted to Prof. S. T. Patil, Assistant Professor, Department of Irrigation
and Drainage Engineering, College of Agricultural Engineering and Technology, Dapoli for
his valuable suggestions and guidance for my research work. I would loose no opportunity to
express our sincere thanks to Mrs. S. S. Nagarkar, Senior Research Assistant, Department of
Soil and Water Conservation Engineering, College of Agricultural Engineering and
Technology, Dapoli for helping soil analysis. I am also thankful to Mr. S. S. Idate,
Laboratory Assistant, Department of Soil and Water Conservation Engineering.
It is my best privilege to express my sincere thanks to Dr. U. S. Mahadkar, Professor
and Head, Department of Agronomy, College of Agriculture, Dr. Balasaheb Sawant Konkan
Krishi Vidyapeeth, Dapoli, for providing rainfall data for the year 2014 and guidance during
project work.
Our devout gratitude is towards all staff members of College of Agriculture
Engineering and Technology, Dapoli and all my colleagues, who have directly and indirectly
helped me to carry out work effectively.
viii
I wish to employ this opportunity to annotate my unsociable regards, thanks and heart
felt good wishes to Miss. Mehendale G. M. for her co-operation for guiding and solving
software problem during my research work.
I fall short of words in expressing my thanks to my dear friends Jagruti, Pradeep sir,
Ganesh, Amit, Mady, Balaji, Mahesh, Sunil and all my senior and juniors for their constant
support and timely help during this project work.
I am also very thankful to my friends and seniors Aniket, Prashant, Sagar sir and
Swapnil sir for providing me research paper during my research work.
I am extremely obliged to acknowledge the love and affection of my beloved parents
Mummy and Pappa, Ajji and elder sister Shubhangi. No words are enough to describe their
efforts in building up my educational career and financial support whenever required. How
can one express complete thanks for the efforts they have taken right from spoon-feeding in
the childhood to the last moment just passed.
Our life is with a “Golden Line” today and I dedicate it to our Associate Dean who
has laid a perfect foundation, by showing me path bright future.
I express my sincere thanks to whom directly and indirectly extended help during the
research work.
Thank You!
Place: CAET, Dapoli (Kothe Swapnil Ajay)
Dated: / /2015
ix
TABLE OF CONTENTS
Sr.
No.
Title Page No.
CANDIDATE‟S DECLARATION iii
CERTIFICATES
1. Research Guide iv
2. Head of Department v
3. Associate Dean vi
ACKNOWLEDGEMENT vii-viii
TABLE OF CONTENTS ix-x
LIST OF TABLES xi
LIST OF FIGURES xii-xii
LIST OF SYMBOLS xiv
LIST OF ABBREVIATIONS xv
ABSTRACT xvi-xvii
1. INTRODUCTION 1-3
2. REVIEW OF LITERATURE 4-9
3. MATERIAL AND METHODS 10-26
3.1 General Description 10
3.1.1 Study area 10
3.1.2 Data collection 10
3.1.3 Runoff Estimation 10
3.2 Pre-analysis and Formulation of Input and Output Data 12
3.3 Software used 12
3.4 Artificial Neural Networks (ANNs) 12
3.4.1 General Information 12
3.4.2 The Biological Neurons 12
3.4.3 Basic concept of Artificial Neural Network (ANN) model 13-17
3.4.3.1 Activation function 14
3.4.3.2 The back propagation algorithm 16
3.4.3.3 Procedure for ANN model simulation 17
3.5 Training procedure for neural network 18-25
3.6 Statistical analysis 25-26
4. RESULTS AND DISCUSSION 27-46
4.1 Runoff Estimation by using Rectangular weir 27
4.2 Runoff Estimation by using ANN Model 28
4.3 ANN with one input 29-42
x
4.3.1 Most Suitable ANN Architectures 32-42
4.4 Observed and Predicted Runoff 43
4.5 Statistical analysis by ANN method 49
5. SUMMARY AND CONCLUSIONS 50-52
5.1 Summary 50-51
5.2 Conclusions 51-52
6. BIBLIOGRAPHY 53-55
7. APPENDICES 56-60
APPENDIX-I
xi
LIST OF TABLES
Table No. Title
Page No.
4.1 Monthly rainfall and runoff observed at Priyadarshini
watershed for year 2010, 2011, 2013 and 2014
27-28
4.2
Statistical performance of various ANN architectures. 29-31
4.3
Most suitable ANN architecture based on statistical
performance
32
4.4 Observed and Predicted Runoff data for 1-48-1 architecture. 43-49
7.1 Four years rainfall- runoff data of Priyadarshini watershed. 56-60
xii
LIST OF FIGURES
Figure
No.
Title Page
No.
3.1 Location map of Priyadarshini watershed 11
3.2 Structure of a biological neuron 13
3.3 Training network inside the neural network 14
3.4 Log sigmoidal transfer function 15
3.5 Architecture of an artificial neuron 16
3.6 Architecture of feed forward multilayer perception (MLP) 17
3.7 Schematic Representation of Artificial Neural Network 18
3.8 Opening window of Matlab 7.9 ANN toolbox 19
3.9 Neural network fitting tool window 19
3.10 Importing of data to Matlab software 20
3.11 Actual importing data window 20
3.12 Dividing window into training, validation and testing 21
3.13 Selection of number of neuron window 21
3.14 Train data by using Levenberg-Marquardt Algorithm 22
3.15 Window displays the progress of network 22
3.16 Saving the results 23
3.17 Performance plot window 23
3.18 Training state window 24
3.19 Function to fit window 24
3.20 Regression plot of neural network 25
4.1 Hydrograph of Date versus observed runoff and predicted runoff for 1-
18-1 architecture
33
4.2 Scatter plot of observed runoff versus predicted runoff for 1-18-1
architecture
33
4.3 Hydrograph of Date versus observed runoff and predicted runoff for 1-
22-1 architecture
34
4.4 Scatter plot of observed runoff versus predicted runoff for 1-22-1 34
xiii
architecture
4.5 Hydrograph of Date versus observed runoff and predicted runoff for 1-
32-1 architecture
35
4.6 Scatter plot of observed runoff versus predicted runoff for 1-32-1
architecture
35
4.7 Hydrograph of Date versus observed runoff and predicted runoff for 1-
34-1 architecture
36
4.8 Scatter plot of observed runoff versus predicted runoff for 1-34-1
architecture
36
4.9 Hydrograph of Date versus observed runoff and predicted runoff for 1-
35-1 architecture
37
4.10 Scatter plot of observed runoff versus predicted runoff for 1-35-1
architecture
37
4.11 Hydrograph of Date versus observed runoff and predicted runoff for 1-
40-1 architecture
38
4.12 Scatter plot of observed runoff versus predicted runoff for 1-40-1
architecture
38
4.13 Hydrograph of Date versus observed runoff and predicted runoff for 1-
41-1 architecture
39
4.14 Scatter plot of observed runoff versus predicted runoff for 1-41-1
architecture
39
4.15 Hydrograph of Date versus observed runoff and predicted runoff for 1-
45-1 architecture
40
4.16 Scatter plot of observed runoff versus predicted runoff for 1-45-1
architecture
40
4.17 Hydrograph of Date versus observed runoff and predicted runoff for 1-
48-1 architecture
41
4.18 Scatter plot of observed runoff versus predicted runoff for 1-48-1
architecture
41
4.19 Hydrograph of Date versus observed runoff and predicted runoff for 1-
65-1 architecture
42
4.20 Scatter plot of observed runoff versus predicted runoff for 1-65-1
architecture
42
xiv
LIST OF SYMBOLS
Symbol Meaning
& And
cm Centimeters
0 C Degree Celsius
0 E East longitude
ha Hectare
hrs Hours
km Kilometer
lit/sec Litre per second
m Meter
mm Millimeter
Mha Million hectare
Mha-m Million hectare per meter
0 N
North longitude
% Percent
m2
Square meter
xv
LIST OF ABBREVIATIONS
Abbreviations Meaning
ANN Artificial neural network
ASCE American Society of Civil Engineers
bn Billion
C. A. E. T. College of Agricultural Engineering and
Technology
CMS Cubic meter per second
COR Correlation
Dr. BSKKV Dr. Balasaheb Sawant Konkan Krishi Vidyapeeth
et al. And other
etc. Etcetera
Engg. Engineering
Fig. Figure
GDP Gross Domestic Product
GRNN Generalised Regression Neural Network
i.e. That is
MARE Mean Absolute Relative Error
MSE Mean Square Error
pp Page number
r Correlation coefficient
R2
Coefficient of Determination
RCC Reinforced Cement Concrete
RMSE Root Mean Square Error
SOM Self Organising Map
Sq. km Square Kilometer
TBPNN Temporal Back Propagation Neural Network
UK United kingdom
UN United Nations
UNICEF United Nations Children‟s Fund
xvi
ABSTRACT
“DEVELOPMENT OF RAINFALL – RUNOFF MODEL USING
ARTIFICIAL NEURAL NETWORK FOR A PRIYADARSHINI
WATERSHED”
by
Swapnil Ajay Kothe
College of Agricultural Engineering and Technology,
Dr. Balasaheb Sawant Konkan Krishi Vidyapeeth, Dapoli.
Dist. Ratnagiri, Maharashtra State (India)
Research Guide : Dr. B. L. Ayare
Department : Soil and Water Conservation Engineering
An artificial neural network is massively parallel distributed information processing
system that has certain characteristics resembling biological neural network of human being.
Artificial Neural Network (ANN) models have been used successfully to model complex non-
linear input-output relationships in an extremely interdisciplinary field. Artificial Neural
Networks (ANNs) have been used for modelling complex hydrological process, such as
rainfall-runoff and have been shown to be one of the most promising tools in Hydrology.
Hydrological modeling is a powerful technique of hydrologic system investigation for both
the research hydrologists and the practicing water resources engineers involved in the
planning and development of integrated approach for management of water resources. In this
project, the observed rainfall and runoff data of four years (i.e. 2010, 2011, 2013 and 2014)
were used as input data for study. In ANN, input data was divided in three segment 70 per
cent, 15 per cent and 15 per cent for training, validation and testing purpose respectively.
Rainfall-runoff models play an important role in water resource management planning. Total
70 numbers of different types of models with various degrees of complexity have been
developed for this purpose. The output from ANN was statistically tested with statistical
parameters, i.e. Root Mean Square Error (RMSE), Mean Absolute Relative Error (MARE),
Coefficient of Determination (R2) and Correlation (r). The models with single input were not
performing well. Total 10 best suitable architectures selected from the 70 model architecture
xvii
which were studied. The 10 best suitable architectures were 1-18-1, 1-22-1, 1-32-1, 1-34-1, 1-
35-1, 1-40-1, 1-41-1, 1-45-1, 1-48-1, 1-65-1. ANN with 1-48-1 architecture is found to be
most suitable which gives 13.4597, 472.0690, 0.8376 and 0.9188 values for Root Mean
Square Error, Mean Absolute Error, Coefficient of Determination (R²) and Correlation (r)
respectively. ANN 1-48-1 architectures can be adopted to estimate runoff from ungauged
watershed with that day rainfall as single input. The result of this project has shown that with
combination of computational efficiency measures and ability of input parameters describes
the physical behaviour of hydro-climatologic variables. Improvement of the model
predictability is possible in artificial neural network environment, with improved structures of
more input, more hidden layer and hidden neurons.
xviii
CHAPTER I
INTRODUCTION
Water is essential for life. Rainfall is vital resource of water. It is also one of the prime
requirements for agriculture, industrial, domestic and recreational activities. Components of
precipitation, resolved into soil moisture and groundwater are the prerequisites for biomass
production and social development in dry areas. The world‟s total water resources are
estimated as 1.36 × 108 M ha-m. About 97.2 per cent of these world water resources are
saline water mainly in oceans, and only 2.8 percent is available as freshwater at any time on
the planet earth. Out of this 2.8 per cent of fresh water, about 2.2 per cent is available as
surface water and 0.6 per cent as ground water. Even out of this 2.2 per cent of surface water,
2.15 per cent is fresh water in glaciers and icecaps and only of the order of 0.01 per cent is
available in lakes and streams, the remaining 0.04 per cent being in other forms. Out of 0.6
per cent of stored ground water, only about 0.25 per cent can be economically extracted with
the present drilling technology. So, rainfall is cheap and prime source of fresh water.
Per capita availability of water is reducing at an alarming rate. In 1950 water
availability per capita was 6042 cubic meter which is reduced to 1545 cubic meter in 2011. It
has been estimated by UN that it will be reduced to 1140 cubic meter in 2050. As per
UNICEF, 2013 estimates 3.4 bn population will be faced with water scarcity in 2025, nearly
40 per cent of the world population will face water scarce in 2050. About 20 per cent of the
world‟s aquifer will be depleted in 2050. It shows that water will be a serious issue in future.
India occupies only 3.28 million sq. km geographical area, which is 2.4 per cent of the
world‟s land area; it supports over 17 per cent of the world‟s population with 4 per cent world
water resources. India also has a livestock population of 500 million, which is about 20 per
cent of the world‟s total livestock population. More than half of these are cattle, forming the
backbone of Indian agriculture. Indian agriculture shows 14.1 per cent share of the total GDP.
Rainfall runoff relationship is an essential component in the process of water resources
evaluation and is considered as a central problem in hydrology. There have been extensive
researches conducted on the rainfall runoff relationship with different methods by various
scientists. The adoption of artificial neural network has added a new dimension to the system
theoretic modelling approach (ASCE, 2000 (a, b)).
Therefore, it is necessary to the estimate runoff in un-gauged watershed for the design
of hydraulic structures, soil conservation structures, water harvesting structures, flood
moderation studies and design of drainage systems etc. A rainfall-runoff model is a
xix
mathematical formulae describing the rainfall - runoff relations of a catchment area. More
precisely, it produces the surface runoff hydrograph as a response to a rainfall hydrograph as
input. In other words, the model calculates the conversion of rainfall into runoff. A rainfall
runoff model can be really helpful in the case of calculating discharge from a basin. The
transformation of rainfall into runoff over a catchment is known to be very complex
hydrological phenomenon, as this process is highly nonlinear, time-varying and spatially
distributed. Over the years researchers have developed many models to simulate this process.
Based on the problem statement and on the complexities involved, these models are
categorized as empirical, black-box, conceptual or physically-based distributed models. The
unit hydrograph, which is a linear rainfall-runoff model is one well-known example of such a
relationship. However, these simpler models normally fail to represent the nonlinear dynamics
inherent in the process of rainfall-runoff transformation which can be done by using Artificial
Neural Networks and fuzzy logic (Rajurkar et al., 2004).
Hydrological modeling is a powerful technique of hydrologic system investigation for
both the research hydrologists and the practicing water resources engineers involved in the
planning and development of integrated approach for management of water resources.
Prediction of runoff is one of the most useful hydrological systems. The prediction may be
used to assess or predict aspects of flooding, aid in reservoir operation, or be used in the
prediction of the transport of water born contamination. Rainfall-runoff models play an
important role in water resource management planning and therefore, different types of
models with various degrees of complexity have been developed for this purpose. Conceptual
rainfall-runoff models have been widely employed in hydrological modeling. Some of the
well-known conceptual models include the Stanford Watershed Model (SWM), the
Xinanjiang Model and the Soil Moisture Accounting and Routing (SMAR) Model. Although
the modelling of runoff has been studied, many aspects of its dynamics are still unclear.
An artificial neural network is massively parallel distributed information processing
system that has certain characteristics resembling biological neural network of human being.
Artificial Neural Network (ANN) models have been used successfully to model complex non-
linear input-output relationships in an extremely interdisciplinary field. The natural behaviour
of hydrological processes is appropriate for the application of ANN method. In recent years,
ANNs have been used intensively for prediction and forecasting in a number of water-related
areas, including water resource study (El-Shafie et al., 2007), prediction of evaporation
(Sudheer et al., 2002), hydrograph simulator, rainfall forecasting. Hence, motivated by the
successful applications in modeling non-linear system behaviors in a wide range of areas, this
xx
study demonstrated the application of Artificial Neural Network (ANN) to predict rainfall-
runoff relationship. Konkan region is long narrow strip on western side of Sahyadri ranges
along 720 Km coastline. It spread between 15º 6' N and 20º 22' N latitude and 72º 39' E and
73º 48' E longitude, covering total geographical area of 3.04 Mha. Konkan region receives
heavy rainfall (annual average rainfall 280 cm) in the monsoon season, but faces scarcity of
water for drinking purposes in the month of April to May. The area under irrigation of the
region is very meager (less than 4 per cent). This is due to undulating terrain with general
slope ranging from 7 to 35 percent and covered with shallow and lateritic soils (64 %), having
low moisture holding capacity and high runoff. Hence, by considering the facts, the present
study was conducted with following objective:-
1) Rainfall-Runoff analysis of Priyadarshini Watershed.
2) Development of rainfall-runoff model using Artificial Neural Network for
Priyadarshini Watershed.
xxi
CHAPTER II
REVIEW OF LITERATURE
This chapter deals with review of literature covering aspect of Rainfall-Runoff
Modeling using an Artificial Neural Network Model.
2.1 Rainfall-Runoff modelling using Artificial Neural Network.
Minns and Hall (1996) studied artificial neural networks as rainfall-runoff model.
They studied a series of numerical experiments, in which flow data were generated from
synthetic storm sequences routed through a conceptual hydrological model consisting of a
single nonlinear reservoir, has demonstrated the (ANNs). Trial with both one and two hidden
layers in the ANN have shown that, although improved performances are achieved with the
extra hidden layer, the additional computational effort does not appear justified for data sets
exhibiting the degree of nonlinear behavior typical of rainfall and sequences from many
catchment areas.
Dawson and Wilby (1998) reviewed an artificial neural network approach to rainfall
runoff modelling. This paper provides a discussion of the development and application of
Artificial Neural Network (ANNs) to flow forecasting in two flood-prone UK catchments
using real hydrometric data. Comparisons were made between the performance of the ANN
and those of conventional flood forecasting systems. The results obtained for validation
forecasts were of comparable quality to those obtained from operational systems for the River
Amber. The ability of the ANN to cope with missing data and to "learn” from the event
currently being forecast in real time makes it an appealing alternative to conventional lumped
or semi-distributed flood forecasting models. However, further research is required to
determine the optimum ANN training period for a given catchment, season and hydrological
contexts.
Sajikumar and Thandaveswara (1999) studied a non-linear rainfall-runoff model using
an artificial neural network. A rainfall- runoff model that can be successfully estimated (i.e.
yielding sufficiently accurate results) using relatively short lengths of data, is desirable for
any basins in general, and the basins of developing countries like India. An artificial neural
network paradigm, known as the temporal back propagation neural network (TBP-NN), is
successfully demonstrated as a monthly rainfall-runoff model in a “scarce data” scenario (i.e.
the effects of using reduced calibration periods on the performance) is compared with
Volterra type Functional Series Models (FSM), utilizing the data of the River Lee (in the UK)
xxii
and the Thuthapuzha River (in Kerala, India). The results confirm the TBN-NN model as
being the most efficient of the black models tested for calibration periods as short as six years.
Maier and Dandy (2000) studied neural networks for the prediction and forecasting of
water resources variables: a review of modeling issues and applications. A review of 43
papers dealing with the use of neural network models for the prediction of forecasting of
water resources variables is undertaken in terms of the modeling process adopted. In all but
two of the papers reviewed, feed forward networks are used. The vast majority of these
networks are trained using the back propagation algorithm. The process of choosing
appropriate stopping criteria & optimising network geometry and internal network parameters
is generally described poorly or carried out inadequately. All of the above factors can result in
non-optimal model performance and an inability to draw meaningful comparisons between
different models.
Sudheer et al. (2002) studied data-driven algorithm for constructing artificial neural
network rainfall-runoff models. The method studies the statistical properties such as cross,
auto and partial- auto-correlation of the data series in identifying a unique input vector that
best represents the process for the basin, and standard algorithm for training. The
methodology has been validated using the data for a river basin in India. The results of the
study are highly promising and indicated that it could significantly reduce the effort and
computational time required in developing an ANN model.
Riad and Mania (2004) has studied Rainfall-Runoff Model Using an Artificial Neural
Network Approach. An ANN was developed and used to model the rainfall-runoff
relationship, in a catchment located in a semiarid climate Ourika basin at Agbalou in
Morocco. The multilayer perceptron (MLP) neural network was chosen for use in that study.
The results and comparative study indicate that the artificial neural network method was more
suitable to predict river runoff than classical regression model.
Rajurkar et al. (2004) studied modeling of the daily rainfall-runoff relationship with
artificial neural network. An approach for modeling daily flows during flood events using
artificial neural network (ANN) is presented. The rainfall runoff process is modeled by
sampling a simple linear (black box) model with the ANN. The study uses data from two
large size catchments in India and five other catchments used earlier by the World
Meteorological Organization (WMO) for inter comparison of the operational hydrological
model. The study demonstrate that the approach adopted herein for modeling produces
reasonably satisfactory results for data of catchment from different geographical locations,
which thus proves its versatility.
xxiii
Avinash et al. (2006) studied Simulation of Runoff and Sediment Yield using
Artificial Neural Networks. They has studied Daily, weekly, ten-daily, and monthly monsoon
runoff and sediment yield from an Indian catchment were simulated using back propagation
artificial neural network (BPANN) technique, and the results compared with the observed and
with those due to single- and multi-input linear transfer function models. Normalising the
input by its maximum for both the pattern and batch learning algorithms in BPANN, the
model parsimony was achieved through network pruning utilising error sensitivity to weight a
criterion, and it was generalised through cross-validation. The performance based on
correlation coefficient and coefficient of efficiency suggested the pattern-learned artificial
neural network (ANN) based runoff simulation to be superior to both single- and multi-input
models in calibration. The single-input models were however superior in verification. The
ANN based sediment-yield models performed better than both single- and multi-input models
in calibration as well as cross-validation/verification.
Chen and Adams (2006) studied integration of artificial neural networks with
conceptual models in rainfall-runoff modeling. A hybrid form of rainfall-runoff models that
integrated artificial neural networks (ANNs) with conceptual models is proposed in that
study. Based on this integrated approach, the spatial variation of rainfall, the homogeneity of
watershed characteristics and their impacts on runoff can be investigated to the development
of a semi-distributed form of conceptual rainfall-runoff models. As a result in each catchment,
the runoff generation and water budget among different runoff components including surface
runoff and groundwater can be simulated with consideration of the spatially distributed model
parameters and rainfall inputs in the runoff routing. Instead of a linear superposition of the
routed runoff output at the entire watershed outlet as traditionally performed in a semi-
distributed form of conceptual models, artificial neural networks as effective tools in
nonlinear mapping are employed to explore nonlinear transformation of the runoff generated
from the individual sub catchment into the total runoff at the entire watershed outlet. The
verification results from the three conceptual models indicated that the approach of
integrating artificial neural network with conceptual models presented and that shows promise
in rainfall-runoff modeling.
Jain and Shrinivasulu (2006) studied integrated approach to model decomposed how
hydrograph using artificial neural network and conceptual techniques. The results obtained in
that study indicate that (a) the rainfall-runoff relationship in a large catchment consists of at
least three or four different mappings corresponding to different dynamics of the underlying
physical processes, (b) an integrated approach that models the different techniques is better
xxiv
than a single ANN in modeling the complex, dynamic, non-linear, and fragmented rainfall
runoff process, (c) a simple model based on the concept of flow recession is better than as
ANN to model the falling limb of a flow hydrograph, and (d) decomposing a flow hydrograph
into the different segments corresponding to the different dynamics based on the physical
concepts is better than using the soft decomposition employed using SOM.
Kalteh (2008) illustrated rainfall-runoff modelling using artificial neural networks
(ANNs): Modeling and understanding. The results indicate that ANNs are promising tools not
only in accurate modeling of complex processes but also in providing insight from the learned
relationship, which would assist the modeler in understanding of the process under
investigation as well as in evaluation of the model.
Yazdani et al. (2009) studied monthly runoff estimation using Artificial Neural
Network (ANN). In that study ANN model was employed for runoff estimation in Plaszjan
River basin in the central part of Iran. The models used are Multiple Perceptron (MLP) and
Recurrent Neural Network (RNN). Different topologies of Neural Networks were created with
change in input layers, nodes as well as in the hidden layer. The best architecture was found
as 7.4.1. Recurrent Neural Network led to better results than Multilayer Perceptron Network.
Also results indicated that ANN is an appropriate technique for monthly runoff estimation in
the selected basin with these networks being also of the capability to show basin response to
rainfall events.
Arslan (2011) has studied Rainfall–Runoff Modeling Based on Artificial Neural
Networks (ANNs). They has studied, the influences of back propagation efficiencies and
enabling /disabling of input dimensions on rainfall –runoff modelling capability of the
artificial neural network was applied by trying different input dimension for Khasa Chai
catchments, this was done for the evaluation of modeling rainfall-runoff in this region.
Twelve model structures were developed, each one with different number of neurons in the
hidden layer to investigate the probability impacts of enabling /disabling rainfall-runoff,
rainfall, average air temperature, evaporation, humidity. For each model the most successful
structure was found depending on the value of correlation coefficient R and the value of mean
square errors MSE at validation stage. The best rainfall-runoff model for Khasa Chai
catchments was concluded with nine input dimension, nine neurons in the hidden layer. The
results of this research has shown that with combination of computational efficiency measures
and ability of input parameters which describe the physical behavior of hydro-climatologic
variables, improvement of the model predictability is possible in artificial neural network
environment.
xxv
El-shafie et al. (2011) has studied Performance of Artificial Neural Network and
Regression Techniques for Rainfall-Runoff Prediction. They aimed to utilize an Artificial
Neural Network (ANN) to predict the rainfall-runoff relationship in a catchment area located
in a Tanakami region of Japan. The study illustrates the applications of the feed forward back
propagation with hyperbolic tangent neurons in the hidden layer and linear neuron in the
output layer was used for rainfall prediction. To evaluate the performance of the proposed
model, three statistical indexes were used, namely; Correlation coefficient (R), mean square
error (MSE) and correlation of determination (R2). The results showed that the feed forward
back propagation Neural Network (ANN) can describe the behaviour of rainfall-runoff
relation more accurately than the classical regression model.
Joshi and Patel (2011) reviewed rainfall-runoff modeling using artificial neural
network (A literature Review). Three neutral network methods, Feed Forward Back
Propagation (FFBP), Radial Basis Function (RBF) and Generalized Regression Neural
Network (GRNN) were employed for rainfall-runoff modeling of Maleshri hydro
meteorological data. It was seen that all three different ANN algorithms compared well with
conventional Multi Linear Regression (MLR) technique. It was seen that only GRNN
technique did not provide negative flow estimations for some observations. The rainfall-
runoff correlograms was successfully used in determination of the input layer node number.
Sarkar and Kumar (2012) have studied Artificial Neural Networks for Event Based
Rainfall-Runoff Modeling. They had examined its applicability to model the event-based
rainfall-runoff process. A case study has been done for Ajay river basin to develop event-
based rainfall-runoff model for the basin to simulate the hourly runoff at Sarath gauging site.
The results demonstrate that ANN models are able to provide a good representation of an
event-based rainfall-runoff process. The two important parameters, when predicting a flood
hydrograph, are the magnitude of the peak discharge and the time to peak discharge. The
developed ANN models have been able to predict this information with great accuracy. They
shows that ANNs can be very efficient in modeling an event-based rainfall-runoff process for
determining the peak discharge and time to the peak discharge very accurately.
Singh et al. (2013) has studied Artificial Neural Networks Based Daily Rainfall-
Runoff Model for an Agricultural Hilly Watershed. In that study, ANN based daily rainfall-
runoff model has been established for an agricultural hilly watershed known as Khunt micro-
watershed located in the district of Almora, Uttarakhand, India. In the development of the
model, daily rainfall and runoff data for the period 1st June to 31th October for years 2005-
2009 were used to train the ANN, and for the years 2010 and 2011 were used for model
xxvi
validation purpose. The performance of the developed model was assessed based on
parameters like root mean square error (RMSE) and correlation coefficient (R). A network
structure resulting in highest value of correlation coefficient and simultaneously in the lowest
value of RMSE was designated as the best performing. Based on these considerations, it was
observed that the performance of the model based on one day lag and two days lag time were
found satisfactory for the study area. However, the model based on the network 5-5-1
structure with 2 days lag was found to have an edge over the model based on 3-3-1 model
structure with one day lag.
Nandgude et al. (2014) has studied Rainfall- Runoff modeling of Small Watershed in
Konkan Region Using Artificial Neural Network. They had concluded that the rainfall-runoff
relationship is one of the most complex hydrologic phenomena and it is based on tremendous
spatial and temporal variability of watershed characteristics, precipitation patterns etc.
Therefore other models were not performing well. ANN 1-12-1 architectures can be adopted
to estimate runoff from un-gauged watershed with rainfall as input. Controlling the runoff
would require a complete assessment of soil erosion and associated non-point source pollution
impacts in the watershed from a long-term perspective.
xxvii
CHAPTER III
MATERIALS AND METHODS
The main purpose of this study is to develop Artificial Neural Networks for
forecasting runoff. This chapter contains the location and climate of study area, collection of
meteorological data, methodology adopted for rainfall modelling using Artificial Neural
Networks (ANNs) models. Procedure used for calibration and validation of the model and
various criteria for evaluating performance of the models.
3.1 General Description
3.1.1 Study area:
The research work was carried out at the Priyadarshini watershed, College of
Agricultural Engineering and Technology, Dr. Balasaheb Sawant Konkan Krishi Vidyapeeth,
Dapoli, Dist- Ratnagiri (M.S.).
The Priyadarshini Watershed is located at 17.1° N latitude, 73.26° E longitudes and
250 m above mean sea level. The region comes under heavy rainfall with average annual
rainfall of 3500 mm. Priyadarshini watershed has 38.72 ha area. The ambient temperature of
the region varies from 7.5 0C to 38.5
0C and relative humidity varies from 55 percent to 99
percent in different seasons. The climate of the region is hot and humid. The region has hilly
topography with highly drainable lateritic type soils. The location of study area is shown in
Fig. 3.1.
3.1.2. Data collection:
Daily rainfall data has been collected from Department of Agronomy, College of
Agriculture, Dapoli.
3.1.3. Runoff:
Runoff was measured at the outlet of Priyadarshini Watershed for a period of June-
October 2010, 2011, 2013 and 2014 by using rectangular weir (RCC nala bandh) with end
contractions at both ends. The formula for computation of discharge through rectangular weir
(RCC nala bandh) with end contractions at both ends is given by the equation 3.1. (Bansal R.
K., 2010)
Q = 0.0184 (L – 0.2H) × H3/2
…(3.1)
Where,
Q = Discharge, lit/sec
L = Length of crest, cm
H= Head over crest, cm
xxviii
Fig. 3.1 Location map of Priyadarshini Watershed.
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3.2 Pre-analysis and Formulation of Input and Output Data
The daily meteorological data of four years (i.e. 2010, 2011, 2013 and 2014) were
collected from Department of Agronomy, College of Agriculture, Dapoli. Due to some
technical problem of instrument, the runoff data of 2012 was not taken. Thus the total number
of samples for four year‟s period was 198. Each 198 samples of observed rainfall and
observed runoff were taken as input data and output data respectively for analysis and model
development purpose.
These 198 samples were distributed as 138 samples (70%) for training, 30 samples
(15%) for validation and 30 samples (15%) for testing purpose.
3.3 Software:
Model has been developed using MATLAB 2009 software available in the laboratory
of Soil and Water Conservation Engineering, College of Agricultural Engineering and
Technology, Dr. B. S. K. K. V., Dapoli.
3.4 Artificial Neural Networks (ANNs)
3.4.1 General
Artificial Neural Networks (ANNs) are inspired by the structure of human brain that is
well suited for complicated task such as runoff prediction, rainfall-runoff modelling, river
flow prediction etc., in hydrologic systems. These neurons were presented as models of
biological neurons and as conceptual components that could perform conceptual task. ANN
has been proven to provide better solutions for simulations and forecasting. Before looking at
the structure of ANN, we need to understand the structure of biological neurons.
3.4.2 The Biological Neurons
The human brain is the most complex computing known device. The brain‟s powerful
thinking of remembering, and problem solving capabilities inspired many scientists to attempt
computer modelling of its operation. There is a close analogy between the structure of a
biological neuron (i.e. a brain or nerve cell) and the processing element (or artificial neurons).
The biological neuron has three types of components that are of particular interest in
understanding an artificial neuron: its dendrites, cell body and axon (Fig. 3.2). The signals are
electric impulses that are transmitted across a synaptic gap by means of chemical process, a
shown in Fig. 3.2. The cell body sums the incoming signals. When sufficient input is
received, the cell fires; that is, it transmits a signal over its axon to other cells. It is often
xxx
supposed that a cell either fires or doesn‟t at any instant of time, so that transmitted signals
can be treated as binary.
Fig. 3.2 Structure of a biological neuron
The transmission of the signal from a particular neuron is accomplished by an action
potential resulting from differential concentration of ions on either side of the neuron‟s axon.
The ions most directly involves are potassium, sodium and chloride. It causes the neuron to
fire producing an output signal. The output signal travels along the axon to other receiving
neurons. The magnitude of the signal sent depends on the amount of chemical released by the
axon and receive by the dendrites.
3.4.3 Basic concept of Artificial Neural Network (ANN) model
Artificial neural network (ANN) is a massively parallel distributed information
processing system that has certain performance characteristics resembling biological neural
network of the human brain (Junsawang et al., 2007). ANN has been developed from a
generalization of mathematical model of human cognition or neural biology. Their
development is based on the following rules:
1. Information processing occurs at many single elements called nodes, also referred to as
units, cells of neurons.
2. Signals are passed between nodes through connection links.
3. Each connection link has as associated weight that represents its connection strength.
4. Each node typically applies a nonlinear transformation called an activation function to
its net input to determine its output signal.
An ANN is a highly interconnected network of many simple processing units called
neurons, which are analogous to the biological neurons in the human brain. The basic building
block of an ANN is the neurons. They receive an input and produced an output, which is to be
xxxi
passed to other neurons in other layers. Neurons having similar characteristics in an ANN are
arranged in groups called layers. The neurons in one layer are connected to those in the
adjacent layers, but not to those in the same layer. The strength of connection between the
neurons in adjacent layers is represented by what is known as „connection strength‟ or
„weights‟.
An ANN normally consists of three layers, an input layer, a hidden layer and an
output layer. Input layer usually receives the input signal values. Neurons in output layer
produce the output signal. ANN is essentially useful for modeling and prediction of uncertain
and complex phenomena. A neural network can be trained from the previous data to forecast
future events, without accurately understanding the physical parameters which influences the
presents and future events. The training network performed in the neural network is shown in
Fig. 3.3:
Fig. 3.3 Training network inside the neural network.
The objective of the present study is to simulate rainfall runoff relationship using
ANN models. The relationship of rainfall-runoff is known to be highly nonlinear and
complex. The rainfall-runoff relationship is one of the most complex hydrologic phenomena
and it is based on tremendous spatial and temporal variability of watershed characteristics,
precipitation patterns etc. Therefore other models were not performing well. Hence it is
needed to study the ANN structure to simulate runoff from rainfall data for particular soil
conservation measure and different cropping pattern in ungauged watershed.
3.4.3.1 Activation function
The activation function of a neuron in a neural network is only processing function. It
is utilized for the limiting the amplitude of the output of a neuron, also known as transfer
xxxii
function is referred to as squashing function as quashes (limits) the permissible amplitude
range to some finite value. It gives in a range of 0 to 1 (Fig 3.4).
a= log sig (n)
Fig. 3.4 Log sigmoidal transfer function.
This activation function is commonly used in the hidden layers of multiplayer ANN
network and it is represented by equation 3.2. The symbol in the square to the right of each
transfer function. These icons replace the general in the network diagram blocks to the
particular activation function being used.
The mathematical expression of the logistic function is given by the equation 3.2.
( )
…(3.2)
An attempt to improve the accuracy is to use data on discharge excess and sum of
rainfall during the last 24 hours from the prediction time is additional input to the network
model.
Other sigmoidal functions also used and they are given by the equation 3.3 and
equation 3.4.
i) Linear function
( )
ii) Hyperbolic tangent equation
( ) ( )
( ) ( ) ( )
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3.4.3.2 The back propagation algorithm
In the present study the back propagation algorithm (Rumelhart and McClelland,
1986) is used in feed –forward ANNs. This means that artificial neurons are organized in
layers and send their signals “forward” and then the error are propagated backwards. The
network receives inputs by neurons in input layer and the output of network is given by the
neurons on an output layer. There may be one or more intermediate hidden layers. The back
propagation algorithm uses supervised learning, which means that provides the algorithm with
examples of inputs and outputs we want the network to compute, and then the error
(difference between actual and expected results) was calculated. The idea of back propagation
algorithm was to reduce this error, until the ANN learns the training data. The training begins
with random weights, and the goal was to adjust them so that the error will be minimum. The
activation function of artificial neurons in ANNs implementation the back propagation
algorithm is a weighted sum (the sum of inputs X multiplied by their respective weights w).
Architecture of artificial neurons is as shown in Fig. 3.5 and architecture of feed forward
multilayer perception is shown in Fig. 3.6:
Fig. 3.5 Architecture of an artificial neuron.
Where,
X1, X2, X3, X4 = Rainfall inputs to ANN
W1, W2, W3, W4 = Weight to the rainfall.
O = Output of ANN.
f = Logistic sigmoidal function
The expression can be written in the mathematical form as follows and it is given by
the equation 3.5:
)),(),3(),2(),2(),3(,,()( DqttQttQtRtRtRDQSRftQ sslll …(3.5)
xxxiv
Where,
T = time of prediction, h; t1 = time period, (3hrs)
t1 = time to incorporate rainfall (in this case, t1=t-4)
R = rainfall intensity, (mh1); Q = discharge, (cumec)
SR = summation of rainfall value from t-8t to t-3ts, (mm/hr)
DQ = discharge excess between Q (t-8ts) and Q (t-3ts),(cumec).
Dq = discharge excess between Q (t-3ts) and Q (t-ts), (cumec)
Fig. 3.6 Architecture of feed forward multilayer perception (MLP).
Where,
X1, X2, X3, X4…….Xn = Rainfall inputs to ANN in input layer.
1, 2, 3, 4, 5 = Number of neurons in hidden layers.
Y = Runoff as output of neuron
3.4.3.3 Procedure for ANN model simulation
To operate ANN initially data will be arranged in one input and output i.e. observed
rainfall in one notepad sheet and observed rainfall in another notepad sheet format. The flow
chart for operation of ANN model is given in Fig. 3.7. Transfer notepad format data as input
for computing estimated output. In the ANN model epoch were set up to 1000 iteration.
Model training will be checked by using square error (MSE). When we the add input as
rainfall and output as observed runoff in neural network toolbox in MATLAB training of the
network automatically stops whenever recommended output in the form of performance plot,
training state plot, fit plot and regression plot. The output from ANN will be statistically
xxxv
tested with the observed runoff by using various statistical parameter viz. RMSE, MARE, and
correlation coefficient (R) by comparing these statistical parameters best ANN architecture
will be selected. (Mehendale G. M., 2013)
Fig. 3.7 Schematic Representation of ANN
3.5 Training procedure for neural network
In the present study network was studied in Matlab7.9 software. Where 70% data
were used for training, 15% for testing and 15% for validation purpose. The flow chart for
steps performed to operate ANN model is shown in Fig.3.7. Training of neurons is carried out
by following steps:
xxxvi
1) Initially open a Matlab 7.9 software as start> Matlab 7.9 Shown in Fig 3.8:
Fig. 3.8 Opening window of Matlab 7.9 ANN toolbox
2) Type „nftool‟ in Command window > Press „Enter‟ key > the window will be display as
shown in Fig. 3.9:
Fig. 3.9 Neural network fitting tool window
xxxvii
3) Click on import data tab and import input and output (target) data as shown in Fig. 3.10
and 3.11.
Fig. 3.10 Importing of data to Matlab software
Fig. 3.11 Actual importing data window
xxxviii
4) Select the percentage of data for training testing and validation as shown in Fig. 3.12.
Fig. 3.12 Dividing window into training, validation and testing
5) Select number of hidden neuron then network will be displayed as shown in Fig. 3.13.
Fig. 3.13 Selection of number of neuron window
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6) Train the network by clicking on Train tab (Fig. 3.14). It will train by using Levenberg-
Marquadt algorithm and data division is random.
Fig. 3.14 Train data by using Levenberg-Marquadt Algorithm
7) After training it will display output in the form of four plots as performance plot
regression, mean square error and training plot as shown in Fig.3.15.
Fig. 3.15 Window displays the progress of network
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8) Save the result by clicking on „Save Results‟ tab as shown in Fig.3.15.
Fig. 3.16 Saving the results in MATLAB 7.9 Software
9) The architecture which gives less mean square error and good regression is selected as a
network for calculating runoff. Fig. 3.17, 3.18, 3.19 and 3.20.
Fig. 3.17 Performance plot window
xli
Fig. 3.18 Training state window
Fig. 3.19 Function to fit window
xlii
Fig. 3.20 Regression plot of neural network
3.6 Statistical analysis:
The selection procedure is based on the following statistics: Correlation (COR), coefficient
of determination (R2), mean absolute relative error (MARE) and root mean square error
(RMSE). (Salunke J. R., 2013)
100
ˆ
1
n
Q
MARE
n
i i
ii
n
i
ii
n
i
ii
R
1
2
1
2
2
)(
)ˆ(
1
.
)ˆˆ()(
)ˆˆ)((
1
22
1
1
n
i
iii
n
i
i
n
i
iiii
QQQQ
QQQQ
COR
xliii
n
RMSE
n
i
ii
2
1
ˆ
Where,
n The number of data.
iQ The observed value.
iQ̂
The predicted value.
Q i The average of observed value.
Q̂ i The average of predicted value.
COR Correlation.
R2 Coefficient of Correlation.
MARE Mean absolute relative error.
RMSE Root mean square error
xliv
CHAPTER IV
RESULTS AND DISCUSSION
This chapter contains formulation or development of Artificial Neural Networks
(ANNs) for runoff prediction of previous four year (2010, 2011, 2013 and 2014) for a
Priyadarshini Watershed, College of Agricultural Engineering and Technology, Dr.
B.S.K.K.V. Dapoli (M.S.), India. The observed rainfall and observed runoff data of previous
four years (2010, 2011, 2013, and 2014) sets were used to train the model network. The
performances of models were evaluated by using various statistical parameters.
Result and discussion is presented in following sequence:
Runoff Estimation by using Rectangular weir
Runoff Estimation by using ANN Model
ANN with one input
Observed and Predicted Runoff
Statistical analysis by ANN method
4.1 Runoff Estimation by using Rectangular weir
Runoff was continuously measured at the outlet of Priyadarshini Watershed for a period of
June-October every year by using rectangular weir (RCC nala bandh) with end contractions at
both ends and it is given in Appendix-I. Monthly rainfall and runoff observed at Priyadarshini
watershed for year 2010, 2011, 2013 and 2014 are given in Table. 4.1.
Table No. 4.1 Monthly rainfall and runoff observed at Priyadarshini watershed for year
2010, 2011, 2013 and 2014.
Sr.
No.
Month Rainfall,
mm
Runoff
Measured,
ha-m
Runoff, mm Percent
runoff, mm
Year 2010
1. June, 2010 1161.4 17.58 453.90 39.50
2. July, 2010 1750 26.53 685.20 39.15
3. August, 2010 688 8.80 227.15 33.01
4. Sept, 2010 905.2 9.15 236.36 26.01
5. October, 2010 126.8 0 0 0
Total 4931.4 1602.61 34.60
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Sr.
No.
Month Rainfall,
mm
Runoff
Measured,
ha-m
Runoff, mm Percent
runoff, mm
Year 2011
1. June, 2011 918.4 3.45 89.18 9.71
2. July, 2011 2034.2 34.16 882.29 43.37
3. August, 2011 1336.1 20.05 517.82 38.75
4. Sept, 2011 524.5 4.80 124.06 23.65
5. October, 2011 115.6 0 0 0
Total 4928.8 1613.35 32.73
Year 2013
1. June, 2013 1713.2 22.28 575.52 33.59
2. July, 2013 1763.7 31.29 808.21 45.82
3. August, 2013 609.4 2.49 64.32 10.55
4. Sept, 2013 282.6 0 0 0
5. October, 2013 365.4 0 0 0
Total 4734.3 1448.05 30.58
Year 2014
1. June, 2014 346.6 0.00 0.00 0.00.
2. July, 2014 1545.7 20.42 527.32 34.11
3. August, 2014 851.9 10.40 266.59 31.29
4. Sept, 2014 595.6 7.01 182.92 30.71
5. October, 2014 22.4 0.00 0.00 0.00
Total 3362.2 976.83 29.05
4.2 Runoff Estimation by using ANN Model
In the present study, Rainfall data was tested by using logistic sigmoid function and trained
with a Levenberg-Marquardt algorithm to estimate runoff by artificial neural network. For this
purpose the neural network toolbox in Matlab 7.9 was used. All events were classified into
training, testing and validation (discussed in section 3.2). Last four years (2010, 2011, 2013
and 2014) input rainfall data and observed runoff data sets were used for operation consist of
total 198 events.
Total 70 model structures were developed with different number of neurons in the hidden
layer in each model to investigate the impact variable enabling of input dimensions on the
xlvi
model performance. Also an investigation of the best number of neurons in the hidden layer
were tested from 1 number to 70 number for example 1-1-1, 1-2-1, 1-3-1, 1-4-1 up to 1-70-1.
These represents 1 input layer, 1 output layer and 1 hidden layer with varying number of
neurons in hidden layer. The numbers of neurons in the hidden layer were increased till
reaching the maximum allowable value. This was done for each mentioned main 70 models. It
is good to mention that, the number of the neurons in the 1st (input) layer in each main model
was changing from each other but the output layer number was the same i.e. 1, therefore the
range (min, max) of the hidden layer neurons numbers was different for most of the models
depending on the input and output dimension. To estimate runoff by ANN model the each
model operation was started by dividing the input and output data into 70% for training, 15%
for validation and 15% for testing.
In this case of neural network up to 70 hidden neurons in hidden layer were studied, as after
70 hidden neurons it gives very high mean square error. The output of the program in Matlab
7.9 for artificial neural network gives mean square error and R² values directly. While other
statistical parameter RMSE were computed statistically as discussed in methodology in
section 3.6.
4.3 ANN with one input
Initially neural network was trained by using single input (rainfall) and single output (runoff)
and data was divided into 70 percent for training, 15 percent for validation and 15 percent for
testing respectively.
Total 10 best suitable architectures selected from the 70 model architecture which were
studied. The 10 best suitable architectures are 1-18-1, 1-22-1, 1-32-1, 1-34-1, 1-35-1, 1-40-1,
1-41-1, 1-45-1, 1-48-1, 1-65-1. Out of these 10 best suitable architectures, the ANN of
architecture 1-48-1 found most suitable for estimation of runoff than any other ANN
architectures (From Table 4.2).
The 1-48-1 ANN architecture gives 13.4597, 472.0640, 0.8376 and 0.9188 values for RMSE,
MAE, R² and r respectively. The results obtained from Table 4.2 and ANN of architecture 1-
48-1 found suitable for estimation of runoff. Other architectures show over estimated or under
estimated results.
xlvii
Table No. 4.2 Statistical performance of various ANN architectures.
Sr. No. ANN
architecture
RMSE MAE R² r
1. 1-1-1 26.9445 1604.7476 0.3495 0.6926
2. 1-2-1 16.5482 923.1794 0.7546 0.8693
3. 1-3-1 18.6775 529.7967 0.7071 0.8440
4. 1-4-1 16.4758 919.4499 0.7567 0.8700
5. 1-5-1 46.8732 2567.3570 -0.9089 0.7038
6. 1-6-1 17.3721 1052.4632 0.7295 0.8552
7. 1-7-1 16.5205 993.5123 0.7554 0.8692
8. 1-8-1 20.0019 812.2400 0.6415 0.8146
9. 1-9-1 34.2889 833.1672 -0.053 0.6424
10. 1-10-1 34.8407 904.5746 -0.0876 0.6307
11. 1-11-1 16.7546 842.2590 0.7484 0.8654
12. 1-12-1 62.2388 6762.6819 -2.4707 0.7985
13. 1-13-1 29.8332 743.8076 0.2025 0.7576
14. 1-14-1 17.7621 810.7652 0.7173 0.8523
15. 1-15-1 49.4704 100.7597 -1.1927 0.5740
16 1-16-1 15.5535 863.6522 0.7832 0.8864
17. 1-17-1 15.9610 794.5448 0.7717 0.8806
18. 1-18-1 14.0803 967.3900 0.8223 0.9074
19. 1-19-1 302.5474 963.3549 -81.0145 0.2704
20. 1-20-1 16.1615 931.9767 0.7659 0.8763
21. 1-21-1 18.2517 946.2198 0.7015 0.8528
22. 1-22-1 14.4823 924.7313 0.8120 0.9023
23. 1-23-1 15.6052 1033.5323 0.7818 0.8843
24. 1-24-1 27.7277 1039.0618 0.3111 0.7348
25. 1-25-1 16.3079 1048.3129 0.7617 0.8732
26. 1-26-1 17.9160 999.9701 0.7124 0.8448
27. 1-27-1 15.1982 455.4921 0.7930 0.8973
28. 1-28-1 53.8500 3224.27 -1.5989 0.4937
29. 1-29-1 29.3330 1148.5803 0.2290 0.7657
Sr. No. ANN RMSE MAE R² r
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architecture
30. 1-30-1 22.5967 718.5019 0.5424 0.8369
31. 1-31-1 17.9913 1032.1621 0.7099 0.8545
32. 1-32-1 14.5599 1026.6548 0.8100 0.9002
33. 1-33-1 23.8757 1182.6645 0.4892 0.7442
34. 1-34-1 14.1348 862.2806 0.8209 0.9066
35. 1-35-1 13.6192 1032.7056 0.8338 0.9136
36. 1-36-1 29.9699 1095.4350 0.1952 0.7453
37. 1-37-1 43.8865 771.8109 0.7256 0.5625
38. 1-38-1 17.9428 1358.4755 0.7115 0.8637
39. 1-39-1 17.5525 1193.5605 0.7239 0.8631
40. 1-40-1 14.0307 590.2260 0.8236 0.9078
41. 1-41-1 14.6514 799.4085 0.8076 0.9002
42. 1-42-1 20.0217 624.0466 0.6408 0.8169
43. 1-43-1 20.1264 1007.5110 0.6338 0.7978
44. 1-44-1 16.4001 903.6658 0.7590 0.8729
45. 1-45-1 14.4142 761.4747 0.8138 0.9021
46. 1-46-1 117.1673 700.3050 -11.3003 0.3124
47. 1-47-1 91.8162 998.6626 -6.6533 -0.0865
48. 1-48-1 13.4597 472.0690 0.8376 0.9188
49. 1-49-1 18.6037 883.9618 0.6898 0.8481
50. 1-50-1 34.0808 530.9210 -0.0406 0.6960
51. 1-51-1 17.6001 948.7819 0.7224 0.8565
52. 1-52-1 37.9051 313.8737 0.2873 0.6387
53. 1-53-1 20.5796 1096.9607 0.6205 0.8401
54. 1-54-1 23.4060 1116.1307 0.5091 0.7285
55. 1-55-1 26.7320 778.9217 0.3597 0.7874
56. 1-56-1 16.1660 786.2770 0.7658 0.8767
57. 1-57-1 19.8354 708.0767 0.6474 0.8277
58. 1-58-1 20.2809 543.2302 0.6314 0.8060
59. 1-59-1 21.5734 736.4091 0.5829 0.7733
Sr. No. ANN
architecture
RMSE MAE R² r
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60. 1-60-1 16.9394 931.1626 0.7428 0.8623
61. 1-61-1 31.0347 1059.2329 0.1370 0.6994
62. 1-62-1 28.9921 854.9661 0.2468 0.7308
63. 1-63-1 72.2442 836.9484 -3.6763 0.3991
64. 1-64-1 25.5113 498.9529 0.4168 0.7364
65. 1-65-1 14.2817 1103.3821 0.8172 0.9057
66. 1-66-1 19.5598 839.1704 0.6572 0.8253
67. 1-67-1 19.3489 892.2280 0.6645 0.8491
68. 1-68-1 21.2489 868.5564 0.5954 0.8158
69. 1-69-1 36.0408 1025.6384 0.1638 0.6425
70. 1-70-1 31.8059 1025.3394 0.093 0.6870
4.3.1 Most suitable ANN Architectures:
Total 10 best suitable architectures selected from the 70 model architecture based on the
statistical parameter and they are given in Table 4.3.
Table No. 4.3 Most suitable ANN architectures based on statistical performance.
Sr. No. ANN
architecture
RMSE MAE R² r
1. 1-18-1 14.0803 967.3900 0.8223 0.9074
2. 1-22-1 14.4823 924.7313 0.8120 0.9023
3. 1-32-1 14.5599 1026.6548 0.8100 0.9002
4. 1-34-1 14.1348 862.2806 0.8209 0.9066
5. 1-35-1 13.6192 1032.7056 0.8338 0.9136
6. 1-40-1 14.0307 590.2260 0.8236 0.9078
7. 1-41-1 14.6514 799.4085 0.8076 0.9002
8. 1-45-1 14.4142 761.4747 0.8138 0.9021
9. 1-48-1 13.4597 472.0690 0.8376 0.9188
10. 1-65-1 14.2817 1103.3821 0.8172 0.9057
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These 10 best suitable architectures represented graphically are as follows:
1) Architecture 1-18-1:
The 1-18-1 ANN architecture gives 14.0803, 967.39, 0.8223 and 0.9074 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-18-1 and it is shown in Fig. 4.1.
As shown in Fig 4.2 the number of scatter points above the average line are more in
number hence the result shows that runoff has been overestimated.
Fig. 4.1: Hydrograph of Date versus observed runoff and predicted runoff for 1-18-1
architecture.
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Predicted Runoff
Linear (Predicted Runoff)
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Fig. 4.2: Scatter plot of observed runoff versus predicted runoff for 1-18-1 architecture.
2) Architecture 1-22-1
The 1-22-1 ANN architecture gives 14.4823, 924.7313, 0.8120 and 0.9023 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-22-1 and it is shown in Fig. 4.3.
As shown in Fig 4.4 the number of scatter points above the average line are more in
number hence the result shows that runoff has been overestimated.
Fig. 4.3: Hydrograph of Date versus observed runoff and predicted runoff for 1-22-1
architecture.
Fig. 4.4: Scatter plot of observed runoff versus predicted runoff for 1-22-1 architecture.
0
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Linear (Predicted Runoff)
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3) Architecture 1-32-1:
The 1-32-1 ANN architecture gives 14.5599, 1026.6548, 0.8100 and 0.9002 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-32-1 and it is shown in Fig. 4.5.
As shown in Fig 4.6 the number of scatter points below the average line are more in
number hence the result shows that runoff has been underestimated.
Fig. 4.5: Hydrograph of Date versus observed runoff and predicted runoff for 1-32-1
architecture.
Fig. 4.6: Scatter plot of observed runoff versus predicted runoff for 1-32-1 architecture.
0
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60
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100
120
140
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180
200
0 50 100 150 200
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Observed Runoff
Predicted Runoff
Linear (Predicted Runoff)
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4) Architecture 1-34-1:
The 1-34-1 ANN architecture gives 14.1348, 862.2806, 0.8209 and 0.9066 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-34-1 and it is shown in Fig. 4.7.
As shown in Fig 4.8 the number of scatter points above the average line are more in
number hence the result shows that runoff has been overestimated.
Fig. 4.7: Hydrograph of Date versus observed runoff and predicted runoff for 1-34-1
architecture.
Fig. 4.8: Scatter plot of observed runoff versus predicted runoff for 1-34-1 architecture.
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150.00
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Observed Runoff
Predicted Runoff
Linear (Predicted Runoff)
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5)
6) Architecture 1-35-1:
The 1-35-1 ANN architecture gives 13.6192, 1032.7056, 0.8338 and 0.9136 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-35-1 and it is shown in Fig. 4.9.
As shown in Fig 4.10 the number of scatter points above the average line are more in
number hence the result shows that runoff has been overestimated.
Fig. 4.9: Hydrograph of Date versus observed runoff and predicted runoff for 1-35-1
architecture.
Fig. 4.10: Scatter plot of observed runoff versus predicted runoff for 1-35-1 architecture.
7) Architecture 1-40-1:
0.00
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40.00
60.00
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100.00
120.00
140.00
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180.00
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Observed Runoff
Predicted Runoff
Linear (Predicted Runoff)
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The 1-40-1 ANN architecture gives 14.0307, 590.2260, 0.8236 and 0.9078 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-40-1 and it is shown in Fig. 4.11.
As shown in Fig 4.12 the number of scatter points above the average line are more in
number hence the result shows that runoff has been overestimated.
Fig. 4.11: Hydrograph of Date versus observed runoff and predicted runoff for 1-40-1
architecture.
Fig. 4.12: Scatter plot of observed runoff versus predicted runoff for 1-40-1 architecture.
8) Architecture 1-41-1:
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20
40
60
80
100
120
140
160
180
200
0 50 100 150 200
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Observed Runoff
Predicted Runoff
Linear (Predicted Runoff)
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The 1-41-1 ANN architecture gives 14.6514, 799.4085, 0.8076 and 0.9002 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-41-1 and it is shown in Fig. 4.13.
As shown in Fig 4.14 the number of scatter points below the average line are more in
number hence the result shows that runoff has been underestimated.
Fig. 4.13: Hydrograph of Date versus observed runoff and predicted runoff for 1-41-1
architecture.
Fig. 4.14: Scatter plot of observed runoff versus predicted runoff for 1-41-1 architecture.
9) Architecture 1-45-1:
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100
150
200
0 50 100 150 200
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Observed Runoff
Predicted Runoff
Linear (Predicted Runoff)
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The 1-45-1 ANN architecture gives 14.4142, 761.4747, 0.8138 and 0.9021 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-45-1 and it is shown in Fig. 4.15.
As shown in Fig 4.16 the number of scatter points below the average line are more in
number hence the result shows that runoff has been underestimated.
Fig. 4.15: Hydrograph of Date versus observed runoff and predicted runoff for 1-45-1
architecture.
Fig. 4.16: Scatter plot of observed runoff versus predicted runoff for 1-45-1 architecture.
10) Architecture 1-48-1:
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Observed Runoff
Predicted Runoff
Linear (Predicted Runoff)
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The 1-48-1 ANN architecture gives 13.4597, 472.0690, 0.8376 and 0.9188 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-48-1 and it is shown in Fig. 4.17.
As shown in Fig 4.18 the number of scatter points above the average line are more in
number hence the result shows that runoff has been overestimated.
Fig. 4.17: Hydrograph of Date versus observed runoff and predicted runoff for 1-48-1
architecture.
Fig. 4.18: Scatter plot of observed runoff versus predicted runoff for 1-48-1 architecture.
11) Architecture 1-65-1:
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Observed Runoff
Predicted Runoff
Linear (Predicted Runoff)
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The 1-65-1 ANN architecture gives 14.2817, 1103.3821, 0.8172 and 0.9057 values for
RMSE, MAE, R² and r respectively. The curve has been plotted for the observed runoff and
predicted runoff of architecture 1-65-1 and it is shown in Fig. 4.19.
As shown in Fig 4.20 the number of scatter points above the average line are more in
number hence the result shows that runoff has been overestimated.
Fig. 4.19: Hydrograph of Date versus observed runoff and predicted runoff for 1-65-1
architecture.
Fig. 4.20: Scatter plot of observed runoff versus predicted runoff for 1-65-1 architecture.
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4.4 Observed and Predicted Runoff:
Last four years (2010, 2011, 2013 and 2014) input observed rainfall data and observed
runoff data sets were used to train the model network. Total 10 best suitable architectures
selected from the 70 model architecture. The 10 best suitable architectures are1-18-1, 1-22-1,
1-32-1, 1-34-1, 1-35-1, 1-40-1, 1-41-1, 1-45-1, 1-48-1, 1-65-1. Out of this 10 model
architectures, ANN model the neural network with 1-48-1 architecture gives better result than
other architectures under study. The observed runoff and predicted runoff of architecture 1-
48-1 is shown in Table 4.4 and the curve has been plotted and it is shown in Fig. 4.17.
As shown in Fig 4.18 the number of scatter points above the average line are more in
number hence the result shows that runoff has been overestimated.
Table No. 4.4 Observed Runoff and Predicted Runoff for 1-48-1 Architecture.
Sr. No. Date Observed Runoff (mm) Predicted Runoff (mm)
1 16-06-2010 21.7 54.26
2 17-06-2010 99.32 110.01
3 18-06-2010 24.17 16.91
4 19-06-2010 185.91 185.91
5 20-06-2010 77.83 3.05
6 21-06-2010 21.2 16.88
7 22-06-2010 11.61 11.25
8 23-06-2010 9.86 15.09
9 24-06-2010 2.3 3.41
10 18-07-2010 6.13 17.79
11 19-07-2010 5.17 15.99
12 20-07-2010 19.66 42.71
13 21-07-2010 54.03 69.69
14 22-07-2010 124.38 109.91
15 23-07-2010 66.71 54.07
16 24-07-2010 31.95 26.90
17 25-07-2010 82.98 76.62
18 26-07-2010 47.45 59.07
19 27-07-2010 68 59.40
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20 28-07-2010 31.72 22.07
Sr. No. Date Observed Runoff (mm) Predicted Runoff (mm)
21 29-07-2010 38.41 28.09
22 30-07-2010 40.6 18.56
23 31-07-2010 68 51.81
24 01-08-2010 62.35 42.05
25 02-08-2010 16.28 10.99
26 03-08-2010 29.49 24.86
27 04-08-2010 2.87 3.99
28 05-08-2010 0.33 1.92
29 06-08-2010 0.07 1.92
30 11-08-2010 0.09 4.80
31 12-08-2010 10.78 11.97
32 18-08-2010 2.4 12.92
33 19-08-2010 10.45 8.01
34 20-08-2010 5.17 10.99
35 24-08-2010 8.56 19.61
36 25-08-2010 18.23 19.59
37 26-08-2010 19.18 20.56
38 27-08-2010 4.9 2.96
39 28-08-2010 6.79 4.84
40 29-08-2010 17.76 9.89
41 30-08-2010 2.1 2.42
42 31-08-2010 3.56 3.56
43 01-09-2010 36.22 36.47
44 02-09-2010 32.28 26.53
45 03-09-2010 5.8 4.28
46 04-09-2010 1.04 2.63
47 05-09-2010 11.8 17.74
48 06-09-2010 40.98 51.22
49 07-09-2010 31.15 12.87
50 08-09-2010 4.15 5.84
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51 09-09-2010 62.15 73.01
Sr. No. Date Observed Runoff (mm) Predicted Runoff (mm)
52 11-09-2010 7.4 2.30
53 12-09-2010 2.76 4.19
54 13-09-2010 0.62 1.95
55 17-06-2011 21.68 27.14
56 18-06-2011 4.88 4.39
57 09-07-2011 8.95 37.91
58 12-07-2011 3.99 11.39
59 13-07-2011 14.64 24.98
60 14-07-2011 57.61 50.84
61 15-07-2011 117.78 110.01
62 16-07-2011 35.86 12.38
63 17-07-2011 67.5 110.00
64 18-07-2011 124.78 121.66
65 19-07-2011 87.94 58.51
66 20-07-2011 19.72 5.56
67 22-07-2011 13.35 15.99
68 23-07-2011 15.08 9.07
69 24-07-2011 5.19 4.23
70 25-07-2011 4.58 7.12
71 26-07-2011 10.88 26.44
72 27-07-2011 8.22 9.41
73 28-07-2011 8.95 10.39
74 29-07-2011 76.36 99.02
75 30-07-2011 97.57 109.94
76 31-07-2011 103.34 112.24
77 01-08-2011 110.9 109.99
78 02-08-2011 33.53 23.13
79 03-08-2011 15.08 25.01
80 04-08-2011 18.29 52.50
81 05-08-2011 2.66 2.26
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82 06-08-2011 1.51 1.93
Sr. No. Date Observed Runoff (mm) Predicted Runoff (mm)
83 07-08-2011 1.73 12.38
84 08-08-2011 1.31 6.47
85 28-08-2011 94.32 143.11
86 29-08-2011 166.49 166.49
87 30-08-2011 55.56 50.47
88 31-08-2011 16.43 9.85
89 01-09-2011 2.17 5.56
90 02-09-2011 69.68 68.30
91 03-09-2011 39.45 24.85
92 04-09-2011 10.48 26.44
93 05-09-2011 1.73 2.01
94 06-09-2011 0.22 2.46
95 07-09-2011 0.33 6.97
96 11-06-2013 34.92 34.85
97 12-06-2013 18.6 16.91
98 14-06-2013 104.28 51.72
99 15-06-2013 60.75 67.54
100 16-06-2013 96.52 96.53
101 17-06-2013 74.23 68.40
102 18-06-2013 53.58 28.16
103 19-06-2013 42.62 62.64
104 20-06-2013 4.53 1.99
105 21-06-2013 15.63 14.31
106 22-06-2013 2.55 3.83
107 23-06-2013 2.08 4.34
108 24-06-2013 1 8.25
109 25-06-2013 25.94 19.99
110 26-06-2013 17.58 10.38
111 27-06-2013 13.93 6.15
112 28-06-2013 1.66 2.96
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113 29-06-2013 2.23 3.89
Sr. No. Date Observed Runoff (mm) Predicted Runoff (mm)
114 30-06-2013 1.09 12.02
115 01-07-2013 11.49 16.91
116 02-07-2013 9.17 27.59
117 03-07-2013 37.06 56.93
118 05-07-2013 8.21 3.83
119 07-07-2013 39.96 9.90
120 08-07-2013 18.41 29.15
121 09-07-2013 28.35 51.83
122 10-07-2013 59.8 29.16
123 11-07-2013 73.24 52.45
124 12-07-2013 82.95 51.78
125 13-07-2013 41.56 34.02
126 14-07-2013 12.75 10.36
127 15-07-2013 8.46 6.80
128 16-07-2013 6.6 3.23
129 17-07-2013 11.63 28.30
130 18-07-2013 32.34 19.29
131 19-07-2013 14.02 13.18
132 20-07-2013 42.8 61.75
133 21-07-2013 37.81 51.83
134 22-07-2013 27.9 56.93
135 23-07-2013 18.28 18.56
136 24-07-2013 100.96 100.99
137 25-07-2013 55.04 26.06
138 26-07-2013 16.96 7.12
139 27-07-2013 7.3 8.97
140 28-07-2013 5.17 7.73
141 25-07-2013 14.2 26.53
142 26-07-2013 36.77 51.78
143 27-07-2013 10.97 13.84
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144 28-07-2013 2.38 1.99
Sr. No. Date Observed Runoff (mm) Predicted Runoff (mm)
145 13-07-2014 19.8 24.89
146 14-07-2014 36.75 38.77
147 15-07-2014 68.95 49.88
148 16-07-2014 96.9 98.50
149 17-07-2014 42.42 39.12
150 18-07-2014 15.52 6.80
151 19-07-2014 5.5 10.87
152 20-07-2014 3.4 8.25
153 21-07-2014 2.1 4.51
154 22-07-2014 26.36 13.83
155 23-07-2014 10.42 8.13
156 24-07-2014 26.68 50.83
157 25-07-2014 9.52 4.28
158 26-07-2014 0.33 3.23
159 27-07-2014 1 3.41
160 28-07-2014 54.09 56.80
161 29-07-2014 27.49 21.39
162 30-07-2014 15.23 13.62
163 31-07-2014 64.86 61.03
164 01-08-2014 55.36 68.08
165 02-08-2014 12.9 2.70
166 03-08-2014 3.35 3.49
167 04-08-2014 14.79 9.36
168 05-08-2014 45.91 44.83
169 06-08-2014 15.38 7.12
170 07-08-2014 6.53 9.82
171 08-08-2014 2.87 3.83
172 09-08-2014 0.05 2.55
173 10-08-2014 4.73 10.11
174 11-08-2014 3.62 4.72
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175 12-08-2014 5.98 14.29
Sr. No. Date Observed Runoff (mm) Predicted Runoff (mm)
176 13-08-2014 1.98 3.97
177 14-08-2014 0.1 2.26
178 15-08-2014 0.03 2.36
179 26-08-2014 0.42 1.94
180 27-08-2014 5.77 9.62
181 28-08-2014 5.5 9.90
182 29-08-2014 0.15 1.95
183 30-08-2014 13.07 1.99
184 31-08-2014 68.1 68.10
185 01-09-2014 45.04 51.93
186 02-09-2014 8.46 3.45
187 03-09-2014 9.27 3.99
188 04-09-2014 13.7 10.58
189 05-09-2014 10.29 23.21
190 06-09-2014 83.18 83.27
191 07-09-2014 4.9 1.93
192 08-09-2014 1.58 1.98
193 09-09-2014 3.48 14.31
194 10-09-2014 0.61 4.23
195 11-09-2014 0.02 10.39
196 12-09-2014 1.58 3.32
197 13-09-2014 0.77 3.71
198 14-09-2014 0.04 1.94
4.5 Statistical analysis by ANN method
After several trials a three layer ANN architecture consisting of one input layer, one
hidden layer and one output layer was found best for data set and for estimation of runoff. The
number of neurons in one input and output layer is up to 70. This resulted 1-48-1 as best
model configuration and indicated that 1 neuron in hidden layer fitted best on test data and
shows a high degree of accuracy with training data set. ANN with above configuration was
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trained several iterations and best result were obtained with 13 iterations on the basis of
minimum percent mean square error (PMSE).
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CHAPTER V
SUMMARY AND CONCLUSIONS
The runoff forecasting is very essential for planning and management of water
resources. The artificial neural network is the most efficient runoff forecasting method.
Artificial Neural Networks (ANNs) are non-linear mapping structures based on the functions
of human brain. ANNs can identify and learn correlated patterns between input data sets and
corresponding target values. The accurate runoff prediction is one of the greatest challenges in
hydrology. Artificial Neural Networks have been proven to be the most successful tool in
dealing with highly complicated problems due to their powerful capability to model non-
linear systems without the need to make any assumptions.
5.1 Summary:
The present study was undertaken with the specific objectives as, to develop rainfall-
runoff model using Artificial Neural Network for a Priyadarshini watershed. Rainfall runoff
relationship was studied by Artificial Neural Network (ANN) using Matlab 7.9 software.
Total 70 numbers of ANN architectures were used for the computation of runoff. Total 10
best suitable architectures selected from the 70 model architecture. The 10 best suitable
architectures are 1-18-1, 1-22-1, 1-32-1, 1-34-1, 1-35-1, 1-40-1, 1-41-1, 1-45-1, 1-48-1, 1-65-
1. Out of these 10 best suitable architectures, the ANN of architecture 1-48-1 found most
suitable for estimation of runoff than any other ANN architectures. ANN with 1-48-1
architecture is found to be better which gives 13.4597, 472.0640, 0.8376 and 0.9188 values
for Root Mean Square Error, Mean Absolute Error, Correlation (r) and Coefficient of
Determination (R²) respectively.
The Artificial Neural Network (ANN) models show an appropriate capability to model
hydrological process. They are useful and powerful tools to handle complex problems
compared with other traditional models. In this study, the results show clearly that the
artificial neural networks are capable of model rainfall runoff relationship in the Priyadarshini
watershed in which the general enhancement achieved by using neural networks in many
other hydrological fields.
The present study also provides a valuable data based on continuous rainfall and
runoff in Priyadarshini Watershed for the year 2010, 2011, 2013 and 2014. Runoff was
continuously measured at the outlet of Priyadarshini Watershed for a period of June-October
2010, 2011, 2013 and 2014 using rectangular weir (RCC nala bandh) with end contractions at
both ends. These data help to understand the complex physical processes in the watershed.
lxix
In the monsoon period of the year 2010 from June to October total rainfall occurred
was 4631.4 mm contributing 1161.4 mm in the month of June followed by 1750 mm,
688 mm, 905.2 mm and 126.8 mm in the month of July, August, September and
October respectively. In the month of June runoff depth was 453.90 mm, 685.20 mm
in July, 227.15 mm in August and 236.36 mm in September were observed. The total
runoff depth was 1602.61 mm and the total runoff found to be 34.60 per cent for the
year 2010.
In the monsoon period of the year 2011 from June to October total rainfall occurred
was 4928.8 mm contributing 918.4 mm in the month of June followed by 2034.2 mm,
1336.1 mm, 524.5 mm and 115.6 mm in the month of July, August, September and
October respectively. In the month of June runoff depth was 89.18 mm, 882.29 mm in
July, 517.82 mm in August and 124.06 mm in September were observed. The total
runoff depth was 1613.35 mm and the total runoff found to be 32.73 per cent for the
year 2011.
In the monsoon period of the year 2013 from June to October total rainfall occurred
was 4734.3 mm contributing 1713.2 mm in the month of June followed by 1763.7
mm, 609.4 mm, 282.6 mm and 365.4 mm in the month of July, August, September
and October respectively. In the month of June runoff depth was 575.52 mm, 808.21
mm in July and 64.32 mm in August were observed. The total runoff depth was
1448.05 mm and the total runoff found to be 30.58 per cent for the year 2013.
In the monsoon period of the year 2014 from June to October total rainfall occurred
was 3362.2 mm contributing 346.6 mm in the month of June followed by 1545.7 mm,
851.9 mm, 595.6 mm and 22.4 mm in the month of July, August, September and
October respectively. In the month of July runoff depth was 527.32 mm, 266.59 mm
in August and 182.92 mm in September were observed. The total runoff depth was
976.83 mm and the total runoff found to be 29.05 per cent for the year 2014.
5.2 Conclusions:
Following conclusion is drawn from above results.
1) Total 70 model structures were developed, each one with different number of neurons
in the hidden layer to investigate the probability impacts of enabling rainfall-runoff.
2) Out of 70 model structure, 10 best suitable models were selected based on statistical
performance. Out of 10 ANN model, the 1-48-1 as best model configuration and
lxx
indicated that 48 neuron in hidden layer fitted best on test data and shows high degree
of accuracy with training data set than other ANN architectures.
3) The performance of ANN 1-48-1 architecture in estimation of runoff from rainfall data
was checked statistically, Hence, this ANN 1-48-1 architectures can be adopted to
estimate runoff from ungauged watershed with rainfall as input.
4) ANN model with 1-48-1 architecture is found to be better which gives 13.4597,
472.0640, 0.8376 and 0.9188 values for Root Mean Square Error, Mean Absolute
Error, Correlation (r) and Coefficient of Determination (R²) respectively.
5) The proposed approach can be a very efficient tool and useful alternative for the
computation of rainfall-runoff relationship.
lxxi
CHAPTER VI
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VII. APPENDICES
APPENDIX I
Table No. 7.1 Four years rainfall- runoff data of Priyadarshini watershed.
Sr. No. Date Observed
Rainfall (mm)
Observed
Runoff (mm) 1 16-06-2010 134 21.7
2 17-06-2010 193.8 99.32
3 18-06-2010 33 24.17
4 19-06-2010 413 185.91
5 20-06-2010 9.6 77.83
6 21-06-2010 50.4 21.2
7 22-06-2010 27 11.61
8 23-06-2010 47 9.86
9 24-06-2010 10.4 2.3
10 18-07-2010 43 6.13
11 19-07-2010 35.2 5.17
12 20-07-2010 100.4 19.66
13 21-07-2010 137.6 54.03
14 22-07-2010 181.4 124.38
15 23-07-2010 87.8 66.71
16 24-07-2010 54 31.95
17 25-07-2010 160 82.98
18 26-07-2010 108.8 47.45
19 27-07-2010 85.4 68.00
20 28-07-2010 45.6 31.72
21 29-07-2010 51.8 38.41
22 30-07-2010 58.6 40.60
23 31-07-2010 155.6 68.00
24 01-08-2010 80.2 62.35
25 02-08-2010 26.6 16.28
26 03-08-2010 51.4 29.49
27 04-08-2010 12.2 2.87
28 05-08-2010 1.2 0.33
29 06-08-2010 0.8 0.07
30 11-08-2010 15 0.09
31 12-08-2010 49.6 10.78
32 18-08-2010 42 2.40
33 19-08-2010 38 10.45
34 20-08-2010 26.6 5.17
35 24-08-2010 46.2 8.56
36 25-08-2010 43.4 18.23
37 26-08-2010 46 19.18
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38 27-08-2010 9.4 4.90
Sr. No. Date Observed
Rainfall (mm)
Observed
Runoff (mm) 39 28-08-2010 15.1 6.79
40 29-08-2010 48.2 17.76
41 30-08-2010 8 2.10
42 31-08-2010 10.8 3.56
43 01-09-2010 99.6 36.22
44 02-09-2010 61.6 32.28
45 03-09-2010 13.4 5.80
46 04-09-2010 8.6 1.04
47 05-09-2010 54.6 11.80
48 06-09-2010 104.4 40.98
49 07-09-2010 47.4 31.15
50 08-09-2010 16.8 4.15
51 09-09-2010 159.6 62.15
52 11-09-2010 7.6 7.40
53 12-09-2010 13 2.76
54 13-09-2010 4.2 0.62
55 17-06-2011 150.4 21.68
56 18-06-2011 13.8 4.88
57 09-07-2011 79.2 8.95
58 12-07-2011 27.2 3.99
59 13-07-2011 71.8 14.64
60 14-07-2011 104 57.61
61 15-07-2011 194.2 117.78
62 16-07-2011 28.4 35.86
63 17-07-2011 189 67.50
64 18-07-2011 141.8 124.78
65 19-07-2011 108.6 87.94
66 20-07-2011 16.4 19.72
67 22-07-2011 35.2 13.35
68 23-07-2011 55.6 15.08
69 24-07-2011 13.2 5.19
70 25-07-2011 18.4 4.58
71 26-07-2011 75 10.88
72 27-07-2011 41.2 8.22
73 28-07-2011 56.6 8.95
74 29-07-2011 163 76.36
75 30-07-2011 182 97.57
76 31-07-2011 141 103.34
77 01-08-2011 184.6 110.90
78 02-08-2011 45 33.53
79 03-08-2011 73.4 15.08
80 04-08-2011 82.6 18.29
81 05-08-2011 7.4 2.66
82 06-08-2011 2.4 1.51
83 07-08-2011 28.4 1.73
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84 08-08-2011 17.6 1.31
Sr. No. Date Observed
Rainfall (mm)
Observed
Runoff (mm) 85 28-08-2011 222 94.32
86 29-08-2011 225 166.49
87 30-08-2011 103.6 55.56
88 31-08-2011 24.1 16.43
89 01-09-2011 16.4 2.17
90 02-09-2011 148.8 69.68
91 03-09-2011 72.4 39.45
92 04-09-2011 75 10.48
93 05-09-2011 5.5 1.73
94 06-09-2011 8.15 0.22
95 07-09-2011 38.4 0.33
96 11-06-2013 208 34.92
97 12-06-2013 33 18.60
98 14-06-2013 128 104.28
99 15-06-2013 116 60.75
100 16-06-2013 218.2 96.52
101 17-06-2013 112.4 74.23
102 18-06-2013 76 53.58
103 19-06-2013 110 42.62
104 20-06-2013 5.2 4.53
105 21-06-2013 36 15.63
106 22-06-2013 11.6 2.55
107 23-06-2013 13.6 2.08
108 24-06-2013 20 1.00
109 25-06-2013 59 25.94
110 26-06-2013 48 17.58
111 27-06-2013 40 13.93
112 28-06-2013 9.4 1.66
113 29-06-2013 11.8 2.23
114 30-06-2013 28 1.09
115 01-07-2013 33 11.49
116 02-07-2013 68.2 9.17
117 03-07-2013 87 37.06
118 05-07-2013 11.6 8.21
119 07-07-2013 49 39.96
120 08-07-2013 65.2 18.41
121 09-07-2013 105 28.35
122 10-07-2013 65 59.80
123 11-07-2013 88.2 73.24
124 12-07-2013 129 82.95
125 13-07-2013 53 41.56
126 14-07-2013 25.4 12.75
127 15-07-2013 18 8.46
128 16-07-2013 10 6.60
129 17-07-2013 63 11.63
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130 18-07-2013 58.8 32.34
Sr. No. Date Observed
Rainfall (mm)
Observed
Runoff (mm) 131 19-07-2013 29.2 14.02
132 20-07-2013 158 42.80
133 21-07-2013 105 37.81
134 22-07-2013 87 27.90
135 23-07-2013 46.4 18.28
136 24-07-2013 170 100.96
137 25-07-2013 70 55.04
138 26-07-2013 18.4 16.96
139 27-07-2013 21.5 7.30
140 28-07-2013 19.2 5.17
141 01-08-2013 61.6 14.20
142 02-08-2013 125 36.77
143 03-08-2013 29.8 10.97
144 04-08-2013 5.2 2.38
145 13-07-2014 73 19.8
146 14-07-2014 92.6 36.75
147 15-07-2014 103 68.95
148 16-07-2014 140 96.9
149 17-07-2014 79.5 42.42
150 18-07-2014 18 15.52
151 19-07-2014 26.4 5.5
152 20-07-2014 20 3.4
153 21-07-2014 14.2 2.1
154 22-07-2014 97.6 26.36
155 23-07-2014 19.8 10.42
156 24-07-2014 82.2 26.68
157 25-07-2014 13.4 9.52
158 26-07-2014 10 0.33
159 27-07-2014 10.4 1
160 28-07-2014 119.6 54.09
161 29-07-2014 45.8 27.49
162 30-07-2014 29.6 15.23
163 31-07-2014 118.2 64.86
164 01-08-2014 112.2 55.36
165 02-08-2014 8.8 12.9
166 03-08-2014 10.6 3.35
167 04-08-2014 22.6 14.79
168 05-08-2014 100.8 45.91
169 06-08-2014 18.4 15.38
170 07-08-2014 24 6.53
171 08-08-2014 11.6 2.87
172 09-08-2014 8.4 0.05
173 10-08-2014 24.8 4.73
174 11-08-2014 14.8 3.62
175 12-08-2014 30.2 5.98
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176 13-08-2014 12.1 1.98
Sr. No. Date Observed
Rainfall (mm)
Observed
Runoff (mm) 177 14-08-2014 7.4 0.1
178 15-08-2014 7.8 0.03
179 26-08-2014 3.4 0.42
180 27-08-2014 23.4 5.77
181 28-08-2014 37.4 5.5
182 29-08-2014 4 0.15
183 30-08-2014 5.2 13.07
184 31-08-2014 335.2 68.1
185 01-09-2014 130.2 45.04
186 02-09-2014 10.5 8.46
187 03-09-2014 12.2 9.27
188 04-09-2014 37.2 13.7
189 05-09-2014 51.2 10.29
190 06-09-2014 206.7 83.18
191 07-09-2014 3 4.9
192 08-09-2014 5 1.58
193 09-09-2014 36 3.48
194 10-09-2014 13.2 0.61
195 11-09-2014 56.6 0.02
196 12-09-2014 10.2 1.58
197 13-09-2014 11.2 0.77
198 14-09-2014 3.6 0.04