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Chapter 1 Introduction

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CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION TO SOFT COMPUTING APPROACHES

Soft Computing is the fusion of methodologies that were designed to model and

enable solutions to real world problems, which are too difficult to model mathematically.

Soft computing is an association of methodologies that provides flexible information

processing capability for handling real-life ambiguous situations (Zadeh, 1994). Its aim is

to exploit the tolerance for imprecision, uncertainty, approximate reasoning and partial

truth in order to achieve tractability, robustness and low-cost solutions (Mitra et al.,

2002) The guiding principle is to devise methods of computation that lead to an

acceptable solution at low cost, by seeking for an approximate solution to an imprecisely

or precisely formulated problem (Pal et al., 1999).

Soft computing differs from conventional (may be called as hard) computing in

various ways. Unlike hard computing, it is tolerant to imprecision, uncertainty, partial

truth and approximation. In Fact, the role model for soft computing is the human mind.

Soft Computing is basically optimization technique to find solution of problems which is

more lingual to reply.

1.1.1 Fuzzy Logic (FL)

‘Fuzzy logic’ was introduced by Sir Lofti Zadeh in 1965 as an extension of

classical set theory and is built around the central concept of a fuzzy set or membership

function. Fuzzy set theory, the proper name for this theory, enables the processing of

imprecise information by means of membership functions, in contrast to Boolean

characteristic mappings. The conventional characteristic mapping φ of a classical set A

(called crisp set) takes only two values: one, when an element belongs to the set; and

zero, when it does not.


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{AxAx

xA ∉∈

=,0,1

)(φ ………………………(1.1)

Where )(xAφ is characteristic function and A is classical set.

Here,

)(xAφ }1,0{∈ Ax ∈∀

{0,1} is a simple set containing only two elements zero and one.

While, in fuzzy set theory, an element can belong to a fuzzy set with its

membership degree μ ranging from zero to one, Fuzzy sets A)

are usually identified

with these membership functions. For an environmental variable X, we can consider the

fuzzy set A)

of acceptable values. If x is a possible value of X, then )(xA)μ denotes its

membership degree in the fuzzy set A)

.

Where,

]1,0[)( ∈xA

)μ Ax

)∈∀ …………………..(1.2)

Here A)

is the fuzzy set of that environmental variable X, [0,1] is a closed interval set in

which all real numbers from zero to one as well as the numbers zero and one are

included.

As fuzzy set theory have a basic concept in mathematics, it is not misunderstood

that it has a tremendous impact on various mathematical disciplines, such as logic,

algebra, data analysis, statistics etc. But more importantly, fuzzy set theory has a vast

numbers of applications that make use of these mathematical disciplines.

In fuzzy rule-based systems, knowledge is represented by if–then rules P => Q.

Fuzzy rules consist of two parts: an antecedent part P stating conditions on the input

variable(s); and a consequent part Q describing the corresponding values of the output

variable(s). Usually, the case of a single output variable is considered. In Mamdani type

models, both antecedent and consequent parts consist of fuzzy statements concerning the

value of the variables, whereas in Sugeno type models, the consequent part expresses a


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non-linear relationship between the input variables and the output variable (Takagi and

Sugeno, 1985).

Bridge between Fuzzy Logic and Weather Forecasting

The Neuro Fuzzy model that is used in this research work is ANFIS. Neuro fuzzy

systems that implement Takagi-Sugeno type fuzzy inference systems get more accurate

results than the approaches that implement neuro fuzzy inference systems of Mamdani

type, although it has a higher bigger computational complexity. As a guide line for

implementing highly efficient neuro-fuzzy systems they should have the following

characteristics such as fast learning, on-line adaptability, self-adjusting with the aim of

obtaining the small global error possible and small computational complexity. This will

help in improving the accuracy of weather forecasting (Yen wee Khun, 2006).

1.1.2 Fuzzy Inference System (FIS)

In order to understand what ANFIS model actually is, consider a Fuzzy Inference

System, as shown in figure1.1, with two inputs x, y and a single output z. It is also

assumed that there are two fuzzy if-then rules which are:

Rule 1: if x is A1 and y is B1 then

1 1 1 1f p x q y r= + + ………………………………(1.3)

Rule 2: if x is A2 and y is B2 then

2 2 2 2f p x q y r= + +……………………………….(1.4)

When the overall output is the weighted average of each rule’s crisp output

induced by the rule’s firing strength (minimum of the degrees of match with the premise

part) and output membership functions then the model is called Tsukamoto Fuzzy Model

(Tsukamoto, 1979).

If overall fuzzy output is derived by applying max operation to the qualified fuzzy

outputs (each of which is equal to the minimum of firing strength and the output

membership function of each rule) then it becomes Mamdani Fuzzy Model.


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Fig. 1.1: A two-rule two-input fuzzy inference System

Various schemes have been proposed to choose the final crisp output based on the

overall fuzzy output; some of them are centroid of area, bisector of area, mean of

maxima, maximum criterion etc (Lee, 1990).

Takagi and Sugeno’s fuzzy if-then rules are used when the output of each rule is a

linear combination of input variables plus a constant term and the final output is the

weighted average of each rule’s output (Jang, 1993). In all the experiments done in this

research, one single output which can be taken as lenear combination of input parameters

therefore in proposed study Type 3 of fuzzy inference System i.e. Takagi and Sugeno’s

Fuzzy Model which is nothing but ANFIS model may be used (Figure 1.1).

1.1.3 Neural Networks (NN)

There are millions of very simple processing elements or neurons in the brain,

linked together in a massively parallel manner. This is believed to be responsible for the

human intelligence and discriminating power [Mitra]. Neural Networks are developed to

try to achieve biological system type performance using a dense interconnection of

simple processing elements analogous to biological neurons. Neural Networks are

information driven rather than data driven [Jain, 1998]. Typically, there are at least two


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layers, an input layer and an output layer. One of the most common networks is the Back

Propagation Network (BPN) which consists of an input layer and an output layer with

one or more intermediate hidden layers [Dhingra, 2011].

Neural Networks are trained to perform a particular function by adjusting the

values of the connections (weights) between elements using a set of examples before they

can be employed to the actual problem. Commonly neural networks are adjusted, or

trained, so that a particular input leads to a specific target output [Ball, 2006]. The

method used to generate the examples to train the network and the training algorithm

employed has a significant impact on the performance of the neural network-based

model. One of the training algorithms used is the Back-Propagation (BP) algorithm. This

algorithm aims to reduce the deviation between the desired objective function value and

the actual objective function value [Dhingra, 2011].

Fig. 1.2: Structural diagram of a biological neuron (top) equivalent to schematic

diagram of the artificial neural network (below)


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Artificial neural networks (ANN) have found wide use in fields areas as signal

processing, pattern recognition, medical diagnosis, speech production, speech

recognition, identification of geophysical features and mortgage evaluation.

Figure 1.2 provides a sketch of a biological neuron and a human-made neuron.

The biological neuron acts as a processing element that receives many signals. These

signals may be modified by a weight at the receiving synapse. Then the processing

element sums the weighted inputs. When the input becomes sufficiently large, the neuron

transmits a single output that goes off to other neurons. The human-made neuron works

by analogy. It takes an input, multiplies it by a weight, adds a bias and then passes the

result through a transfer function. Several neurons in parallel are known as a layer.

Adding these layers together produces the neural network. The weights and bias values

are optimized to produce the desired output.

1.1.4 Hybridization of Neuro Fuzzy Systems

During the last few years there has been a large and energetic upswing in research

efforts aimed at synthesizing fuzzy logic with neural networks. Neural networks possess

advantages in areas such as reasoning on a high (semantic or linguistic) level. The two

technologies nicely complement each other.

Neural networks and fuzzy systems individually have reached a degree of

maturity where they are applied to real world situations. Researchers often utilize these

two technologies in series, using one as preprocessor of postprocessor for the other.

Examples include the use of fuzzy inputs and outputs for neural networks, the use of

neural networks to quantify the shape of a fuzzy membership functions and so on.

At present, there is no generally accepted theory or methodology for the design of

neural networks and the process uses is generally a trial-and-error approach based on the

experience of the designer. The complexity of neural networks design arises from the

high dimensional, heterogeneous space that must be explored by the system. The primary

features that are of concern in the design of neural networks are the structure of the

network, the inputs to the network and the specifications of the learning algorithm

parameters. All of these quantities are problem specific. While there are guidelines based

on experience that can be very helpful in design, some mathematical based procedure

would also be very helpful.


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The neural methods and fuzzy systems are brought in both for the purpose of

identifying rules and membership functions and for adaption of a fuzzy system to a

changing physical system and its environment. The approach is known in the literature as

neural network driven fuzzy reasoning. For both expert knowledge elicitation and

adaptation, the underlying strategy is to identify certain parameters of fuzzy systems and

use neural networks to induce and/or adjust them.

Although, fuzzy logic and artificial neural networks are both functionally and

structurally different, it is concluded that the synthesis of these two areas will give rise to

a new paradigm called fuzzy neural networks. The latter have the potential to capture the

benefits of the fields, fuzzy logic and neural networks, into a single paradigm.

Fuzzy logic and neural networks complement each other, and their unification

provides the benefits of both the technologies. A brief comparison between fuzzy logic

and neural networks from the point of knowledge acquisitions, uncertainty, reasoning,

adaption and natural language processing is shown in Table 1.1. The merging of these

two fields results in an emerging paradigm called “fuzzy neural networks” or “fuzzy-

neural systems”.

Table 1.1: Comparison between Fuzzy Systems and Neural Networks

Using fuzzy operators and connectives in the mathematical operations of an

artificial neuron can develop fuzzy neural networks with the following features:

• Easy to implement natural language so that the structure of knowledge base is very

clear and efficient.

Property Skills Fuzzy System Neural Networks Knowledge Acquisition Input Tools Human Experts

Interaction Sample Sets Algorithms

Uncertainty Information Cognition

Quantitative and Qualitative Decision

Making

Quantitative Perception

Reasoning Mechanism Speed Heuristic Search Low

Parallel Computing High

Adaption Fault-Tolerance Learning

Low Induction

Very High Adjusting Synaptic Weights

Natural Language

Implementation Flexibility

Explicit High

Implicit Low


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• Any changes in the task and environment can be very easily taken care of by adapting

the weights of the neural network.

• Since a fuzzy system is one kind of interpolation, drastic reduction of data and

software/hardware and overheads can be achieved.

Neuro–Fuzzy Approaches

Presently, the neuro–fuzzy approach is becoming one of the major areas of

interest because it gets the benefits of neural networks as well as of fuzzy logic systems

and it removes the individual disadvantages by combining them on the common features.

Different architectures of neuro-fuzzy system have been investigated by number of

researchers such as (Lin, 1994), (Medsker, 1995) and (Jana, 1996). These architectures

have been applied in many applications especially in the process control.

Neural networks and fuzzy logic have some common features such as distributed

representation of knowledge, model–free estimation, ability to handle data with

uncertainty and imprecision etc.

Fuzzy Logic provides a structure within which the learning ability of neural

networks is employed. In this field there are a number of possible uses. Firstly, neural

networks can be used to generate the membership functions for a fuzzy system and to

tune them; a schematic for this is shown in Fig. 1.3.

Fig. 1.3: Neuro-Fuzzy Systems for tuning a Membership Function

Neural Network automatically generates additional fuzzy rules and membership

functions, to meet certain specifications and reduce design time and costs. Fuzzy logic

Fuzzy System

Input Output

Neural Network


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enhances the generalization capability of a neural network system by providing more

reliable output when extrapolation is needed beyond the limits of the training data. The

architecture of neuro-fuzzy system is shown in Figure 1.4.

Fig. 1.4: Schematic Diagram of a Neuro-Fuzzy System

The system contains the following three layers:

• Fuzzification layer

• Fuzzy rule layer

• Defuzzification layer

In a fuzzification layer each neuron represents an input membership function of

the antecedent of a fuzzy rule. In the fuzzy inference layer fuzzy rules are fired and the

value at the end of each rule represents the initial weight of the rule and will be adjusted

to its appropriate level at end of training. In the Defuzzification layer each neuron

represents a consequent proposition and its membership function can be implemented by

combining one or two sigmoid functions and linear functions. The weight of each output

link here represents the centre of gravity of each output membership function of the

consequent and is trainable. After getting the corresponding output the adjustment is

made in the connection weights and the membership functions in order to compensate the

error and produce a new control signal.

The Neural Network fine tunes the output of the Fuzzy System according to what

it has learned about, users’ personal preferences from the fine adjustments they have

previously made. Explicit knowledge acquired from experts can be easily incorporated

into such a system and implicit knowledge can be learned from training samples to

enhance the accuracy of the output. There are also many other ways to combine neural

and fuzzy techniques to improve the learning speed, adjust learning etc.

Fuzzification Layer

Fuzzy Rule Layer

Defuzzification Layer

Input Output


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1.1.5 Adaptive Neuro Fuzzy Inference Systems (ANFIS)

A general neural network, connection weights and propagation and activation

functions of Neuro Fuzzy is different a lot when it is compared to a simple neural

network (Jang, 2004). Neuro Fuzzy inference system has some special characteristic

described as the follows:

• ANFIS can be represented as a set of fuzzy rules at anytime of the learning

process. Therefore the Neuro Fuzzy systems can be created without prior

knowledge of creating fuzzy rules.

• ANFIS is based on a fuzzy system which is trained by set of data that learns from

neural network theory. This approach only takes into account available data to

make changes in the membership function in the fuzzy system.

• The learning procedure is constrained to ensure the semantic properties of

underlying Neuro Fuzzy.

• A Neuro Fuzzy is represented as special three-layer feed forward neural Network.

Architecture of ANFIS

The ANFIS stands for Adaptive Network based Fuzzy Inference System or

Adaptive Neuro Fuzzy Inference System. ANFIS implements a Takagi Sugeno fuzzy

inference system and it has five layers as shown in Figure 1.5.

Fig. 1.5: First-order Sugeno fuzzy model


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Layer 1: Every node in this layer 1, ,( 1,4)iO i = is membership degree of , ( 1, 2)iA i = and

2 , ( 3, 4)iB i− = and it gives the degree to which x (or y) satisfy 1 2 1 2, ( , )A A orB B .

Membership Function for 2,i iA B − may be any of the following functions:

1. Triangular Membership function: It is a three parameters function defined as:

0,

,( : , , )

,

0,

x ax a a x bb atriangle x a b cc x b x cc b

c x

≤⎧ ⎫⎪ ⎪−⎪ ⎪≤ ≤⎪ ⎪−= ⎨ ⎬−⎪ ⎪≤ ≤⎪ ⎪−⎪ ⎪≤⎩ ⎭ ………………….(1.5)

2. Trapezoidal Membership function: It requires four parameters to be defined:

0,

,

( : , , , ) 1,

,

0,

x ax a a x bb a

trapezoid x a b c d b x cd x c x dd c

d x

≤⎧ ⎫⎪ ⎪−⎪ ⎪≤ ≤

−⎪ ⎪⎪ ⎪= ≤ ≤⎨ ⎬⎪ ⎪−⎪ ⎪≤ ≤

−⎪ ⎪⎪ ⎪≤⎩ ⎭…………………....(1.6)

3. GaussianMFs : it is specified by two parameters as:

212( ; , )

x c

gaussian x c e σσ−⎛ ⎞− ⎜ ⎟

⎝ ⎠= …………………...……..(1.7)

4. Generalized Bell: Also called simply bell MF , is defined as:

21( ; , , )

1bbell x a b c

x ca

=−+

5. Sigmoid MF: it is defined as:

( )1( ; , ) ,

1 expsig x a c

a x c=

+ − −⎡ ⎤⎣ ⎦

……….…………….(1.8)

.….…………….(1.9)


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Where a controls the slope at x=c.

In the proposed research, Model A1 is generalized bell function and

1 21( )

1A bx

x ca

μ =−+

………………………(1.10)

Where {a, b, c} is the non- linear parameter set and is called premise parameter set.

Changing the values of a, b, c will change the shape of bell function.

Layer2: Its nodes O2, i are represented by Π

2, ( ) ( ), 1,2i ii i A BO w x y iμ μ= = =

…….…………….(1.11)

Here each node output represents the firing strength of a rule.

Layer 3: Its nodes O3, I are represented by N, Normalized Firing Strength.

3,

1 2

, 1, 2ii i

wO w iw w

= = =+ …………………..(1.12)

Layer 4: Its nodes O4, I are calculated as:

4, . ( ), 1,2i i i i i i iO w f w p x q y r i= = + + = ………………..(1.13)

Where iw is normalized firing strength from layer 3and the set {pi, qi , ri } is Lenear

parameter set called consequent parameter of this adaptive node.

Layer 5: This is a single node layerΣ. Overall Output f is given by equation (1.14)

5,1

..

i ii

i ii i

i

w ff O w f

w= = =

∑∑ ∑

………….……….(1.14)


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1.2 STATISTICAL CURVE FITTING MODELS

Statistical methods are those methods that use observations from past looking for

repetitions of same patterns in the future.

Consider the output variable, the variable to be forecasted i.e. Precipitation can be

represented by a single column vector Y and the set of input variables Temperature (dry-

wet), Vapor Pressure, Relative Humidity, Pan Evaporation (mm) etc be represented by

(P.A. Bogenschutz, 2004) a multidimensional vector X,

Where,

X= (X1, X2, X3, ……, Xn)

n is the total number of input variables.

A relation between X and Y variables can be made:

Y= D + C1 X1+C2X 2+ C3 X3 +……………….+Cn Xn ………. (1.15)

Where C1, C2, C3,………, Cn and D all are constants (may be negative or zero).

In the proposed research, MatLab tool is used to fit and plot a multidimensional

surface on the same data used to forecast precipitation by ANFIS model.

This method is based on statistical approaches such as regression and auto

regressive integrated moving average techniques. The regression equations are used to

predict weather parameters. Knowledge of correlation coefficient will also help to access

effect of one parameter over the other. In the proposed research, four models have been

discussed and analyzed to forecast precipitation as described in further sub-sections.

1.2.1 Linear Model

Linear model plays vital role in the prediction of local monsoonal precipitation.

Important characteristics of linear model are:

• Linear model accounts only for main effects.

• It requires at least four experiments.

• It is the default model in MatLab. It contains linear combination of variables in X

vector.


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Let us assume that xi and xj are two variables in X vector then the equation for

output y in Linear model is given by

Y=∑cixi+∑cjxj ……….…… (1.16)

Or

Y= c1x1+c2x2+……..+cnxn …………….(1.17)

Where c1, c2, c3 ….. cn are all non-zero constants.

1.2.2 Quadratic Model

Quadratic model has the following properties due to which it can be used for

calculating beta vales for the value of output Y:

• Quadratic model accounts for response curvature

• It requires at least ten experiments

In Quadratic model, the square of the variable i.e. xi2 and xj

2 and the product of xi

and xj is used.

The equation to calculate the value of Y is

Y=∑ai xi2 +∑bi xj

2 +∑ci xi . xj +∑cixi …….……. (1.18)

It can have constants ai, bi, ci, linear terms xi, their linear cross products xi, xj

terms and squared terms xi2.

Linear vs. Quadratic Effects

Linear function

• Only two levels are sufficient.

• Theoretical basis for all two-level designs.


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Quadratic function

• Three levels are needed to quantify quadratic effect.

• Two-level design with center points confounds quadratic effects.

• Two levels adequate to detect quadratic effect.

1.2.3 Pure Quadratic Model

It includes constants ci, linear terms xi, and squared terms xi2. The equation to calculate

the value of Y is

Y=∑ai xi2 +∑bi xj

2 +∑cixi ………………………… (1.19)

1.2.4 Interactive Model

It contains constants ci, linear terms xi, and their linear cross products xi xj terms.

• Interactive model includes binary interactions.

• It requires at least seven experiments.

The equation to calculate the value of Y is

Y=∑ci xi . xj +∑cixi ……………………………. (1.20)

1.3 MatLab Toolbox

In this research work two MatLab toolboxes (anfisedit, rstool) are used which are

explained in brief in further subsections.

1.3.1 Anfis Editor (anfisedit)

In this section, ANFIS Editor GUI in the MatLab toolbox is discussed whose syntax is

$ anfis

In fuzzy inference GUIs, it is required to manually choose the shape of the

membership functions depending upon the parameters. By changing these parameters

there will change in the shape of the membership function. In some modeling situations,

there is no way to decide the shape of membership functions simply from looking at data.

Rather than choosing the parameters associated with a given membership function

arbitrarily, these parameters could be chosen from the input/output data. In such cases,


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the Fuzzy Logic Toolbox neuro-adaptive learning techniques incorporated in the anfis

command may be used.

ANFIS derives its name from Adaptive Neuro-Fuzzy Inference System. Using a

given input/output data set, the toolbox function anfis constructs a Fuzzy Inference

System (FIS) whose membership function parameters are adjusted using either a back

propagation algorithm alone or in combination with a least squares type of method called

hybridization. The anfis function can be accessed either from the command line or

through the ANFIS Editor GUI. However the functionality of the command line function

anfis and the ANFIS Editor GUI is similar, they are used somewhat interchangeably in

this discussion.

Training Adaptive Neuro Fuzzy Inference Systems Using the ANFIS Editor GUI

To start the GUI, type the following command at the MATLAB prompt:

$ anfisedit

The ANFIS Editor GUI window will open and have to perform the following tasks:

A. Loading, Plotting, and Clearing the Data

B. Generating or Loading the Initial FIS Structure

C. Training the FIS

D. Validating the Trained FIS

A. Loading, Plotting, and Clearing the Data

In order to load an initial input data set, the following steps are used:

• First of all, the data Type is specified.

• Then the input data is selected from a file saved in the computer or already loaded in

the MatLab workspace (as shown in figure 1.6 )

Fig. 1.6: Input Data as variable name hisar_test_data


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• Then by clicking Load Data, data is loaded as input in anfis editor. After loading the

data, it will be displayed in the plot. The training, testing and checking data are shown

in blue as circles, dots, and pluses respectively as shown in figure 1.7

Fig. 1.7: Training, Testing and Checking data Graph as circles, dots, and pluses

To clear a specific data set from the GUI:

• In the Load data area, the data Type of which we want to clear the data, is selected.

• Then by clicking ‘Clear Data’ the data, training, testing or checking data will be

cleared from anfis editor. However it will remain in workspace.

This action also removes the corresponding data from the plot.

B. Generating or Loading the Initial FIS Structure

After loading the data, there is need to describe an initial FIS model structure. It

can be done by either of the following ways:

• Load a previously saved Sugeno-type FIS structure from a file on disk

• Or load an FIS from MatLab workspace.


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• Or Generate the initial FIS model by choosing one of the following partitioning

techniques:

o Grid partition— It generates a single-output Sugeno-type FIS by using grid

partitioning on the data.

o Subtractive Clustering — it generates an initial model for ANFIS training by first

applying subtractive clustering on the data.

By clicking the ‘Structure’ a graphical representation of the initial FIS model

structure can be seen which is shown in figure 1.8.

Fig. 1.8: Structure of ANFIS Model with six inputs and one output

C. Training the FIS

After loading the training data and generating the initial FIS structure, training of

FIS can be started. The following steps show how to train the FIS:

• In Optim. Method, choose hybrid or back propagation as the optimization method.

The optimization methods train the membership function parameters to emulate the

training data. The hybrid optimization method is a combination of least-squares and

back propagation gradient descent method.


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• Enter the number of training Epochs and the training Error Tolerance to set the

stopping criteria for training. The training process stops whenever the maximum

epoch number is reached or the training error goal is achieved.

• By clicking train now to train the FIS. This action adjusts the membership function

parameters and displays the error plots shown in figure 1.9.

D. Validating the Trained FIS

After the FIS is trained, validate the model using a testing that differs from the

one used to train the FIS. To validate the trained FIS:

• Select the validation data set and click Load Data.

• Click Test Now. This action plots the test data against the FIS output (shown by red

dots in figure 1.10).

Fig. 1.9: Training the ANFIS model with 100 epochs


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Fig. 1.10: Comparison of Testing data (.) and observed output(*)

1.3.2 Multi-Dimensional Response Surface Tool (rstool)

In MatLab, to fit a multidimensional surface the command available is

rstool(x, y,model)

rstool is response surface tool which fit and plot a multidimensional surface. rstool (x, y,

model, alpha) is a polynomial fit to (x, y) data.

Where X is multidimensional input vector, Sample multidimensional vector X is

shown in table 1.2 which is nothing but an (n x 4) matrix where n is the number of

indices i.e. SMW taken into consideration from 1970-2010. Y is single output column

that contains the variable to be forecasted, Sample Vector Y is shown in table 1.3 which

is a column matrix of order n x 1. The confidence level for predictions is 100(1 -

alpha)%. The default value for alpha is 0.05, which produces 95% (= (100(1-0.05) %)

confidence level and the model may be ‘Linear’ (constant and linear terms), ‘Interaction’

(linear model plus interaction terms), ‘Quadratic’ (interaction model plus quadratic

terms), ‘Pure Quadratic’ (quadratic model minus interaction terms).


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First of all the data is stored as X and Y Matrix in the folder workspace as shown

in Figure 1.11. By typing the command rstool (X, Y) in command window of MatLab, it

produces the lenear model plot of Y shown in figure 1.12. In figure 1.12, a

multidimensional response surface is plotted against four input X1, X2, X3, X4 versus

output Y. The Default model is taken as linear. And beta values, residual and rmse are

exported as a matrix in workspace which is shown in table 1.3, 1.4, 1.5 respectively.

And thus the equation for linear model as

Y= 35.6865823478271- 1.24274917987369 X1 + 0.583439010815411 X2

- 0.123370553850116 X3 - 0.910902294373251 X4 ………………..(1.21)

With root mean squared error RMSE as 25.3644.

Table 1.2: Sample Multidimensional Vector X (First Four Column) and

Sample Vector Y (Last Column)

Temp. Difference Vapor Pressure Relative Humidity Pan Evap Rain Fall 14.9 17.87857 34.14286 7.742857 30 15.17143 20.14286 28.42857 8.614286 5 12.91429 20.49286 24.14286 9.771429 3 12.55714 23.30714 26.42857 5.942857 10 14.32857 22.42857 26.71429 9.471429 2 12.85714 22.34286 28.71429 8.228571 18 11.27143 23.5 22 5.583333 90 9.171429 25.64286 16.71429 6.25 38 8.042857 24.2 14.42857 3.714286 21 9.414286 22.41429 22.42857 5.871429 4 11.62857 22.42143 28.14286 4.714286 41 9.342857 24.09286 17.57143 6.342857 80 9.071429 23.60714 30.14286 4.114286 34 11.02857 23.13571 20.57143 5.385714 4

10.1 24.97857 21.14286 4.514286 7 13.01429 23.71429 26.14286 5.357143 4 15.78571 18.00714 34.57143 5.571429 22 10.52857 18.63571 19.57143 3.314286 65 12.22857 17.54286 30.28571 2.971429 3


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Fig. 1.11: X and Y data saved in workspace

Fig. 1.12: Multidimensional Response Surface Plot of Predicted Variable Y


23

Table 1.4: MatLab Variable Residuals

Table 1.3: Beta Values

Table 1.5: MatLab Variable RMSE


24

1.4 INTRODUCTION TO AGROMETEOROLOGICAL WEATHER

The word agriculture has been derivative from the Latin language from ager

(which means a field) and cultura (which means cultivation). Hence, agriculture is not

only the production of crops but also include processing of fruits and vegetables in the

form of tomato sauce, pickles, jam etc; marketing and use of foods, fibers and by-

products from plants, crops and animals. India is still exemplified by a dominance of

small and marginal farmer (almost 68 percent) and 75 percent of the farm holding are

below 2 hectares. (Gupta D, 2012).

Approximately, one-third of the world’s population was employed in agriculture

in 2007.The weather is the most important components of a country’s physical

environment, which determines the National GDP. So, it is most important to understand

the effect of weather on the life processes of plants and animals and to optimize food

production through understanding of crop-weather interactions and by minimizing losses

through weather Forecasting (Niwas R. et al, 2006).

1.4.1 Terminologies Used in Weather Forecasting

Weather

It refers to the physical state of atmosphere (envelop of gasses surrounding the

earth) at a given time over a place. Weather may be defined as instantaneous condition

of atmosphere over a place. It is highly variable and constantly changing from hour to

hour or day to day. The entity that determines the state of weather is called as

parameter/element of weather such as Temperature, Relative Humidity, Evap-

transpiration, Rainfall etc.. These weather elements are not independent rather they are

correlated to each other.

Meteorology

Meteorology is the branch of science, which study day-to-day atmospheric

conditions. It may be defined as the physics of atmosphere or the science, which

studies weather. Meteorology is the science, which study the physical processes

occurring in the atmosphere, those produce weather.


25

Agricultural Meteorology

Agricultural meteorology is the branch of meteorology which studies the impact

of weather on agricultural farming. It may be defined as the science which studies the

interaction between weather and agriculture including field crops, horticultural crops,

vegetables, animal husbandry etc. G.S.L.H.V. Prasada Rao defined agricultural

meteorology as the science which deals with the influence of weather on crop husbandry

and animal husbandry.

1.4.2 CONSTRAINTS IN WEATHER FORECASTING

Over the last decade, Local Monsoonal Perception (LMP) forecast have improved

greatly in accuracy because of the availability of satellite data, numerical models and

real-time computer system. These forecast tools are highly impressive, but have the

following limitations.

Area Constraint

Till now, Local Monsoonal Perception (LMP) forecast are issued for relatively large

area covering countries and major cities. However local weather can vary considerably

within the area to which LMP is being forecasted. Local area which is very flat reduces

wind disturbance and absorb rainwater deeply into the soil. Depending on wind direction

and season, local atmosphere may be hydrated and moderated.

Because every region is exceptional to some degree, it may be believed that

computer-assisted forecasting could be improved if, as a last step, the process were

refined by an expert system that could take better account of local climatic modifiers. For

this purpose soft computing approach mainly Neuro-Fuzzy may be used in order to

discard such type of problems.

Time Constraint

Available forecasts are based on observations that may be eight hours old and

dataset for most of Automatic Weather Station (AWS) may be Because of this lag time, it

may be concluded that data obsolescence will continue to be a compromising factor for

the foreseeable future and this lag will continue till the validation of observed and

predicted value resulting a big difference in measurement of errors.


26

In this situation, it is required that available public forecasts could become more

reliable if, they will be adjusted by an intelligent system that could take better account of

current and changing local conditions.

Subjectivity

Discovering and understanding the dynamic phenomena of weather, to accurately

predict different weather events, has been an integral component of our study. The

weather data, being inherently fuzzy in nature, requires highly complex processing based

on human observations, satellite photography, followed by computer simulations. This is

further combined with an understanding of the principles of global and local weather

dynamics.

Global warming effect

Weather forecasting has been a very important issue through last two decades. As

we know due to global warming and human interference in nature has made the

predication of climate, a totally unpredictable. We need to have a new approach which

can predicate about the trend of weather- rain, Min temperature, Max temperature, Bright

Sun Shine Hours, Humidity etc.

Change in Atmospheric conditions

Atmospheric conditions change rapidly. Hence, even with sophisticated computer

models, satellite images and monitoring stations across most of the planet, forecasts may

not be exact. That is, sometimes the weather is more predictable than at other times.

1.4.3 Weather Elements

Any entity that controls the weather is called as weather element or weather

parameter. Given below are various parameters which individually (or in combination)

control the weather:

• Solar radiation

• Temperature

• Air Pressure

• Wind

• Sunshine

• Humidity


27

• Cloudiness

• Precipitation etc.

All these elements are highly variable and constitute the weather. Day to day or

hour to hour changes in weather is mainly the result of variations in the amount, intensity

and distribution over earth of weather elements listed above.

1.4.4 Importance of Weather Elements

The weather elements constitute a physical environment in which an organism or

a plant grows. Success or failure of a bio-system depends upon the weather conditions.

The rate of growth and development of a bio-system largely depends upon its ambient

temperature and moisture. The management and execution of agricultural farm practices

is also weather dependent. The maximum efficiency of farm practices can be achieved

with the knowledge of forecasting the weather parameters in anticipation. This has also

been proved in the project of DST named Economic Impact of Agro Advisory Services

(EIAAS)1 done in Department of AgriMet, HAU, Hisar, Haryana completed in Mar,

2007.

1.4.5 Effects of Weather Elements on Crops

Effect of Temperature

If the days are warm, it is good for photosynthesis but if nights are warm, the loss

of respiration is higher. High night temperature favors growth of shoots and leaves and

also affects plant metabolism. Plants, which are adapted to hot climate, if exposed to low

temperature for some time, are found to be killed or injured. Some effects of chilling are

development of yellowing condition in sugarcane, sorghum and maize in winter months

when night temperature is below 200C. When the plants are exposed to very low

temperature, water freezes into ice crystals in intercellular spaces of the plants and

resulting into the death of cells e.g. frost damages in potato, brinjal etc. The temperature

range of 10- 400C is the favorable range for crop plants. The plant cells get killed

when they are exposed to the temperature range from 50 to 60 0C. This point of

1 The researcher has worked as JRF in the above mentioned project.


28

temperature called thermal death point. This varies from plant to plant and species to

species. Higher temperature disturbs the physiological activities like photosynthesis and

respiration. Higher temperature increases respiration leading to rapid depletion of

reserved food. It also increases transpiration loss of water and causes water deficit in crop

plants under limited water supply.

Effect of Moisture

Its presence in the atmosphere plays a significant role. An abundance of moisture

results in a rich natural flora and makes possible a wide choice of crops. Deficiency of

moisture, on the other hand, permits only narrow range of potential crops and is

accompanied by hazards to efficient crop production. The presence of moisture in

atmosphere is termed as humidity. Increasing relative humidity decreases the rate of

transpiration. Reduction in transpiration reduces the translocation of food material and

uptake of nutrients. The relative humidity ranges from 60 to 80 per cent is good for crop

growth. A very high relative humidity is beneficial to maize, sorghum, sugarcane and it is

harmful to gram, sunflower and tobacco. Humidity also affects the water requirement

through evapotranspiration. High humidity with high temperature favors the outbreak of

pest and disease. Too much water may be harmful to plants just as too little. High soil

moisture and humidity condition cause failure in establishing stand of legumes and

grasses. Excess of soil moisture in earlier growing season may result in more vegetative

growth and delayed flowering.

Effect of Rainfall

Rainfall spread is very uneven. Some area is desert receives less than 12 cm and

some places receive more than 1000 cm rainfall. Rain fed crops directly depends on rain.

The water source such as rivers, tanks and wells, which supply water for irrigation also

depend on the rain. Rain occurring during the flowering and grain filling period is very

harmful. After the spray it reduces the efficiency of agrochemical. Heavy rain induces

soil erosion and leaching of nutrient. Deficient rain causes drought and limits the crop

growth and production.


29

1.4.6 Weather Elements Used In the Research: Definition and Measurements

1.4.6.1 Temperature

Temperature is a measure of the heat concept of a body. It shows the intensity of

heat energy or degree of hotness or coldness. The temperature may be defined as the

intensity aspect of heat energy. The temperature measures the average kinetic energy of

the molecules. It is the measures of sensible heat energy of a system. Most widely used

scales for the measurement of temperature is:

Celsius scale: This scale is named for the Swedish astronomer Anders Celsius. It is

internationally accepted for measurement of temperature. The boiling point of water is

100 0C and freezing point of water (Triple point) is 0 0C

Fahrenheit scale: The Fahrenheit scale is used for temperature as evident from historical

records of temperatures in English speaking countries. The freezing point (triple point) of

water is 00F and boiling point of water is 212 0F.

In this research data used for temperature is in 0C.

Instruments for the Measurement of Air Temperature

o Thermometer: The most common instrument for measuring temperature is mercury-

in glass thermometer. Alcohol-in-glass thermometer is also used for measuring

temperature.

o Minimum thermometer: It is an alcohol in glass thermometer with a dark dumbbell

shaped index placed in the bore below top of the alcohol column. It is used to

measure minimum temperature.

o Maximum thermometer: It is mercury in glass thermometer with a constriction in

bore near bulb. It is used for measuring maximum temperature.

1.4.6.2 Actual Vapour Pressure

Pressure of air at a given place is the force exerted against a surface by

continuous collision of gas molecules. Pressure may be defined as the force per unit

surface area.


30

…………..(1.22)

Where,

P = Pressure

F = Force

A = Area upon which force is exerted.

Air pressure is the force exerted in all directions as a result of weight of all the

air above it. Force exerted by mass of a column of air above a given point is called air

pressure.

................................(1.23)

Since,

..............................(1.24)

Where

…………………..(1.25)

………………………..(1.26)

Where,

ρ = Density of liquid (Mercury=1.3×103 kg m-3)

h = Height of liquid (Mercury height =76 cm)

g = Acceleration due to gravity (980 cm s-2)

Vapour Pressure is the partial pressure exerted by water vapour in air. If we sum

up all partial pressures caused by each atmospheric constituent, then it is called

atmospheric pressure (P).

P = ρ (N2) + ρ (O2) + ρ (H2O) + ρ (Ar) + ρ (Co2) + ....... ……..(1.27)

Where,

ρ (N2 ) = Partial pressure due to nitrogen

ρ (O2 ) = Partial pressure due to oxygen


31

ρ (H2 O)= Partial pressure due to water vapour

ρ (Ar) = Partial pressure due to argon

ρ (CO2) = Partial pressure due to carbon dioxide

Actual Vapour Pressure (AVP) is the partial pressure exerted by water vapour

in given volume of air at a given temperature. Actual vapour pressure is called as

saturated vapour pressure when air is saturated. It may also be defined as the pressure

exerted by water vapour actually present in air. It is the saturated vapour pressure at dew

point.

Most widely used units for the measurement of Air Pressure is:

• Height of Hg i.e. inches, cm or mm of Hg.

• Bar: It is the force equal to 106 dynes per square centimeter.

• Pascle (Pa) : It is the force of 1 Newton per square meter = N/m2

• Atmosphere = 1 atm = 29.92 inches or 76 cm or 760 mm of Hg

In this research Data of Actual Vapor Pressure has the unit mm of Hg

Instruments for the Measurement of Air Pressure

o Anemometer: The instrument which is used to measure wind velocity is called as

Anemometer e.g. wind cup anemometer, automatic anemometer etc.

o Anemograph: The instrument which gives a continuous record of wind velocity with

time on a chart.

o Wind vane: The instrument which is used to measure wind direction is known as

wind vane.

o Aero-vane: The instrument, which measures both wind velocity and wind direction.

1.4.6.3 Humidity and Evaporation

Humidity represents the presence of water vapour in air at a time and place.

Water vapour constitutes only a small proportion of air which varies from nearly zero to

maximum of 4 per cent by volume. Water changes its states: solid, liquid and gas from


32

one to another through the process of melting, evaporation, condensation, sublimation

and freezing

Evaporation is a process by which water in liquid form changes to gaseous form.

It may be defined as the water loss in vapour form from a soil/water surface. The energy

used in this process is called as latent heat. The energy of 540 cal/g of water is used in

this process.

Absolute Humidity (AH) may be defined as the mass of water vapour per unit

volume of air or it is the ratio of mass of water vapour to the volume of air. The unit is

g/cm3.

…………….…..(1.28)

Relative Humidity (RH) is defined as ratio of the mass of water vapour present

in air at a temperature to the mass of maximum water vapour which that air can hold at

the same temperature. It may also be defined as the ratio of actual vapour pressure to the

saturated water vapour pressure.

…… (1.29)

Or

………………………….…… (1.30)

Where,

AVP = Actual vapour pressure

SVP = Saturated vapour pressure

Evapotranspiration (ET) is the water loss in vapour form from a water surface or land

surface is called as evaporation. While, the loss of water in vapour form from plants is

known as transpiration. A combination of evaporation and transpiration is termed as

evapotranspiration. Evapotranspiration is combined loss of water in vapour form soil and

plants surface. In a crop field, the rate of water loss through evaporation is higher during

initial phase of crop development and water loss through transpiration is higher during


33

latter period of crop cycle. The rate of evapotranspiration is highest during maximum

ground cover by canopy i.e. maximum leaf area period.

Instruments for Measurement of Evapotranspiration

o Psychrometer: It is an instrument which consists of dry and wet bulb thermometer.

From the dry and wet bulb temperatures, relative humidity, dew point can be found

out and vapour pressure can be found using psychometric tables. It is of two types i.e.

Assmann psychrometer and whirling psychrometer.

o Hygrometer: The instrument used for measurement of humidity is called

hygrometer. One of the types of hygrometer is hair hygrograph.

o Evaporimeter: The instrument which is used to measure evaporation is called as

Evaporimeter. One of the types of Evaporimeter is U.S.A. class-I open pan

Evaporimeter.

o Lysimeter: It is an instrument used for measuring evapotranspiration. It is a direct

method of evapotranspiration estimation. It is of two types:

Weighing type lysimeter. An iron tank is filled with soil uniformly so as the soil profile

may not be disturbed and placed on a balance installed in the ground in the middle of

field. Crop is sown in the tank with the same agronomic practices, which are followed in

the crop filled. The change in weight of the tank is recorded on weighing balance. Then

evapotranspiration is calculated as:

ET (mm) = ΔW×0.6+rainfall (mm) …………….(1.31)

Where ΔW is change in weight.

Volumetric lysimeter measures the evapotranspiration in volumetric term.

Evapotranspiration is calculated by recording change in inflow and outflow of water from

reservoir i.e. a measured amount of water is added in the reservoir.

ET (mm) = Water added in reservoir (litre) x 0.7+ rainfall ………….(1.32)

1.4.6.4 Precipitation

Precipitation may be defined as condensed moisture in liquid or solid forms

falling to the earth surface. The atmospheric moisture precipitates to the earth surface in


34

different solid or liquid forms. Precipitation is measured in inches, centimeters and

millimeters. All the forms of precipitation are termed as hydrometeors. The form of

condensed atmospheric moisture which falls to the earth surface depends upon the

following conditions:

Dew point or condensation temperature

Conditions of atmosphere through which particles pass

Types of clouds

Processes which result precipitation

Rain is the precipitation in the form of liquid water drops having diameters more than

0.5 mm. The precipitation in the form of smaller, widely scattered drops of water is also

called rain. In heavy rains, the rain drops are larger and more in number. Some time rain

drops evaporate completely in the atmosphere before reaching ground. The streaks of

rainfall are called virga.

Conventional precipitation/rainfall is the precipitation, which results due to thermal

convection of warm and moist air masses. Rain, snow and hails are associated with this

type of rainfall.

1.5 BRIEF DETAIL OF INDIAN MONSOONS

The monsoon has always been of critical importance to the people of India since

crops all over the country are dependent on the Local Monsoonal Precipitation (LMP) for

irrigation and livelihood. The southwest monsoon is generally expected to begin around

the middle of June and dies down by September. It begins first in the coastal state of

Kerala and moves upwards at a rate of roughly 1-2 weeks per state. The monsoon

accounts for 80 percent of the rainfall in the country. Indian agriculture (which accounts

for 25 percent of the National GDP and employs 70 percent of the population) is heavily

dependent on the rains, especially crops like cotton, rice, oilseeds and coarse grains. A

delay of a few days in the arrival of the monsoon can badly affect the economy, as

evidenced in the numerous droughts in India in the 90’s (Surender S. et al, 2003).


35

1.5.1 South West Monsoon (SW Monsoon)

During the hot, dry season (April-May) when temperature rises rapidly and

pressures over land decrease, the warm and moist air forms over the adjacent seas starts

blowing, towards the above mentioned low pressure centre. However, in the beginning

the air masses are drawn only from a short distance. But by the end of May or the first

week of June, when the low pressure centre has fully developed, the pressure - gradient is

steepened so that even the trade winds from southern hemisphere are drawn towards the

thermal low positioned in north-western region of the sub-continent. The southerly trade

winds on crossing the equator are deflected to their right.

Fig. 1.13 Normal Dates of Onset and withdrawal of SW Monsoon, INDIA


36

Now, the originally south-east trade winds become south-westerly blowing

towards north-east. In India, the onset of the southwest monsoon for a particular area is

expected in June or July, depending on its location as shown in Figure 1.13. The normal

rainfall during this season over India is about 88.0 cm. South-westerly on-shore winds

blowing towards the centre of low pressure over northern India traverse thousands of

miles over the warm tropical ocean. They are, therefore, full of moisture and have a great

potential for heavy precipitation. The south-west monsoon, as it is called in this region, is

split into two branches by the shape of Peninsular India. They are known as:

• The Arabian Sea branch

• The Bay of Bengal Branch

1.5.2 Experimental Forecast Agencies

Experimental forecast for the year 2010, south-west monsoon rainfall based on

the Indian Meteorological Department (IMD)’s dynamical forecast system was generated.

For this purpose, observed sea surface temperature data of March have been used. In

addition, IMD has also taken into account the experimental forecasts prepared by the

national institutes like Indian Institute of Tropical Meteorology, Pune, Indian Institute of

Science, Bangalore, Space Applications Centre, Ahmadabad, National Aerospace

Laboratories (NAL), Bangalore and Centre for Mathematical Modelling and Computer

Simulation (CMMACS), Bangalore, National Centre for Medium Range Weather

Forecasting (NCMRWF), Noida and operational/experimental forecasts prepared by

international institutes like the National Centers for Environmental Prediction (NCEP),

USA, International Research Institute for Climate and Society (IRI), USA,

Meteorological Office, UK, the European Center for Medium Range Weather

Forecasts(ECMWF), UK and the Experimental Climate Prediction Center (ECPC), USA.

1.6 WEATHER FORECASTING FOR AGRICULTURE

Weather forecasting is foretelling the coming weather in advance. It may be

defined as advance information about the probable weather conditions for few days

to follow. So the time for which weather forecast is made is also important. It can be

termed as lead time. The accuracy of a forecast decreases with increasing lead period and


37

decreasing area under forecast. Different weather phenomena can be forecasted with

different lead time.

1.6.1 Types of Weather Forecasts

On the basis of advance time span, forecast can be grouped into three categories

as shown in figure 1.14.

Fig. 1.14: Types of Weather Forecast

(source HAU, Agromet)

1.6.2 Brief Detail of Haryana’s Monsoon

Haryana is located in the northwest part of the country and the climate is arid to

semi arid with average rainfall of 455 mm. Around 80 per cent rainfall is received during

the month from July to September, Known as south-west monsoon, whose onset and

offset dates are shown in figure 1.15 and the remaining rainfall is received during

December to February.


38

Fig. 1.15 Normal Dates of Onset and withdrawal of SW Monsoon, HARYANA

(source HAU, Agromet data)


39

There are two agro climatic zones in the state. The north eastern part is suitable for

paddy, wheat, vegetable and temperate fruits and the south western part is suitable for

cotton, wheat, mustard, pulses, tropical fruits, exotic vegetables and herbal and medicinal

plants. The state of Haryana extends between 27°39' to 30°55'N latitude and 74°27' to

77°36'E longitude. The altitude in the state ranges between 200 to 300 meters above

mean sea level (except the hilly ranges of Shivaliks in the north and Aravallis in the

south). It is one of the smaller states in the country with an area of 42,222 sq km and is

land locked from all sides and mostly covers the Indo-Gangetic plains.

Fig. 1.16: Annual Rainfall Zones in Haryana

(source HAU, Agromet data)


40

1.6.3 Rainfall in Haryana

Normal annual rainfall features (Figure 1.16) show that amount of annual rainfall

in the state ranges between below 400 mm (south-western parts) to 1200 mm (northern

parts Shivalik foothills) with 25 to 45 per cent coefficient of variation. Above 80 per cent

of this rainfall is received during monsoon season (July to September) which coincides

with the growing season of Kharif crops.

On an average around 300 mm of rains are received during this period in the

south-western (SW) region and above 750 mm in the northern most region with

coefficient of variation ranging between 45 to 55 per cent. Only 10 to 15 per cent of the

annual rainfall is received during October to March period coinciding with the growing

season of rabi crops.

1.7 INTRODUCTION TO PROPOSED RESEARCH WORK

Since last decade soft computing approach has emerged as an advanced

technology with successful applications in many fields. Weather forecasting is the

application of soft computing which combines science and nature to predict the state of

weather for future at a given location.

Soft computing is an innovative approach to construct computationally intelligent

systems that are supposed to processes human like expertise within a specific domain,

adapt themselves and learn to do better in changing environments and explain how they

make decisions. The weather forecasting model based on soft computing is easy to

implement and produces desirable forecasting result by training on the given dataset

(Abraham et al, 2004).

Neuro Fuzzy is a combination of Artificial Neural Network and Fuzzy Logic in

such a way that Neural Network learning algorithms are used to determine the parameters

of Neuro Fuzzy. That is why Neuro Fuzzy is well suited to the problem of weather

forecasting and improve the weather forecasting accuracy.

In this research work, Neuro Fuzzy approach is applied on various weather

forecasting parameters with different data sets and the result is compared with classical

statistical curve fitting methods. Result shows that Neuro Fuzzy approach is much


41

adaptive on all data sets and provides better approximation to Monsoonal Precipitation

value which is taken as output variable. Measurement of performance is taken as Root

Mean Squared Error (RMSE) value which is 4.3633e-04 as compared to RMSE in best

statistical curve fitting model (Linear Mode) which is 3.3939e-02.

1.7.1 Research Aim

The aim of this research is to find out how well the proposed soft computing

models are able to understand the behavior of input parameters so that local monsoonal

precipitation’s prediction can be made. This would help us to anticipate with maximum

degree of confidence level, the general pattern of Monsoonal rainfall in coming season.

1.7.2 Significance of The Research

Local Monsoonal Precipitation (LMP) forecasting greatly contributes towards

making short term adjustments in daily farming activities, which minimize losses due to

adverse weather conditions and improve the yield and quality of agricultural products.

Precipitation forecast is very important because it can be used to protect life and property.

Rain forecasts based on temperature, wind speed and relative humidity are very

important attributes in agriculture sector as well as many industries which largely depend

on the weather condition. For example, heavy rains and flood may cause disaster, an

extended period of dry weather may cause drought and same can be think about for

pilots, fishermen, mountain climbers etc. Therefore, having accurate precipitation

forecasting information may allow these stakeholders to make good decision on

managing their activities.

1.7.3 Organization of the Thesis

The entire research work is divided into five chapters along with the references

used and list of publications.

The first chapter is introductory chapter which describe background substance for

the research problem. It describes in detail various soft computing approaches including

fuzzy logic, fuzzy inference systems, neuro fuzzy approaches and then Adaptive Neuro

Fuzzy Inference Systems, which is the basic model used in the research work done to

forecast the Monsoonal Precipitation. This chapter also provides bridge between fuzzy


42

logic and weather forecasting. Then the chapter contains a brief idea of statistical curve

fitting models such as Linear, Quadratic, Pure Quadratic and Interactive Models. All

MatLab Toolboxes that are used in doing this research work has been explained very

clearly in order to present a very clear idea of how forecasting is done. In this chapter

itself Brief information of Weather Terminologies, its elements and there measurement

instruments is provided so that the raw data collection knowledge is enhanced. Then a

brief detail on Indian Monsoon and lastly Haryana Monsoon detail is given.

The second chapter is endowed with review of literature available in the area of

monsoonal weather forecasting for agriculture. In short, this chapter discussed about the

literature review of weather forecasting, Statistical curve fitting and ANFIS model to

provide a better understanding to choose the best technique to forecast monsoonal

precipitation before proceeding to the research methodology used and experiment and

implementation process. Besides that, gaps of weather forecasting which are a big

hindrance in developing an appropriate model have also been discussed in order to use as

a reference to this thesis report. Based on these gaps we have decided some objectives to

be achieved in this research which are explained in last section of this chapter. On the

basis of these objectives, the Research Methodology will be described in next chapter.

The third chapter describes the research methodology that is used to model the

ANFIS architecture in order to forecast Local Monsoonal Precipitation. This chapter

includes Methods of data collection, Primary source of data, setup of Neuro fuzzy model

and their hybridization learning algorithm. Moreover means of error performance that is

MSE, RMSE, and Output Deviation are also defined in this chapter.

The forth chapter is dedicated to all the Experiments done in MatLab, SPSS,

Excel Sheet along with discussion of results of all these experiments on the basis of

minimum error rate. First of all the values of all input and output variables are shown in

tabular form to have a brief idea regarding the raw data. Then the data is analysed and

processed to make it normalized. This chapter has mainly two sections, 4.4 and 4.5. In

section 4.4 all the experiments have been done using rstool MatLab toolbox in order to

find the best statistical model that have minimum output deviation. In section 4.5

Experiments are done using anfisedit toolbox of MatLab. This section includes only those

experiments which are successful to forecast the Precipitation. Last part of this chapter


43

contains result discussion and comparison. In this part result of all the successful Models

is shown with their output and conclusion. At last, comparison between Statistical Model

and ANFIS Model for the minimum error is done in order to find the final conclusion and

essence of the research.

The fifth chapter is the essence of the thesis which is the conclusion part. It

provides in detail the conclusion, contribution of this whole study in various fields and

scope for further research.

At last, references and list of publications are given.

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