geoststistics

GEOSTATISTICS IN
GEOINFORMATICS
FOR MANAGING
SPATIAL
VARIABILITY
BY;
CHANDSAB NADAF
PGS13AGR6085

INTRODUCTION
HISTORY
APPLICATIONS OF GIS AND RS
SPATIAL SAMPLING DESIGNS
CONCLUSION
Case Studies

INTRODUCTION
High productivity and growth rates achieved during the
Green Revolution era are no longer being sustained to
meet the needs of still increasing population in the
country.
Past growth sources have nearly exhausted and there is
also no scope for expansion of crop land.
Unless we look beyond what we have with modern
technologies for improving productivity.
 Shrinking natural resource base
 Declining quality of resources and
 Environmental degradation issues
will imply increasing threat to our ability to meet the basic
needs of the growing population of the country.

• Recent development in the field of
geoinformatics particularly in the field of
Satellite Remote Sensing, GIS and GPS
technologies have special advantage.
• These information would enable us to
provide valuable scientific insights into
the factors contributing to the low
productivity which in turn would form the
essential ingredients to evolve site
specific suitable and effective strategies
to enhance it.

 It is the science and technology of gathering,
analysing, interpreting, distributing and using
geographic information.
IT INCLUDES
 Surveying and mapping,
 Geographic information systems (GIS)
 Remote sensing, and
 Global Positioning System.

DEFINITIONS
GIOGRAPHICAL INFORMATION SYSTEM:
 “ A powerful set of tools for collecting, retrieving, as well
transforming and displaying spatial data from the real
world for a particular set of purpose ” (Burroughs,1987)
 GIS is most useful when used to perform data analysis
(Lee and Wong, 2001,)
 GIS “ A spatial data handling system” (Marble et al 1983)

#
REMOTE SENSING
DEFINITIONS
“RS is the science/technique of deriving
information about the earth’s land and water
areas from images ( or point/line sample at a
distance) “
“RS is covering the collection of the data about
objects which are not in contact with the
collecting device” (Parker, 1962)

HISTORYHISTORY
Geographical informationGeographical information
system:system:
 1960 – computer based GIS began to be1960 – computer based GIS began to be
usedused
 Pioneer in the development of GIS wasPioneer in the development of GIS was
in Canada (N. America)in Canada (N. America)
 Roger Tomlinson - father of CanadianRoger Tomlinson - father of Canadian
GISGIS
 Previously been used in naturalPreviously been used in natural
resources and environmental researchresources and environmental research

Traditional
GIS
MAP TYPEWRITER
MANUAL
DRAFTING TOOLS
New GIS
COMPUTER PLOTTER CD-ROM

The technology of modern
remote sensing began with
the invention of the camera
more than 150 years ago.
In the 1840s pictures were
taken from cameras
secured to tied balloons.
REMOTE SENSING HISTORY:

Indian remote sensing programme
First resource technology satellite(LAND SAT) was launched in
1972.
Remote sensing technology in India got further boost following the
successful launch of Aryabhata in 1975.
Bhaskara -1 and Bhaskara -2 are launched to carry out remote
sensing on experimental basis in 1979 and 1981.
The first Indian remote sensing satellite, IRS-1A was launched in
1988.
Subsequent to IRS-1A, more satellites namely IRS-1B, IRS-P2,
IRS-1C, IRS-P3, IRS-1D and IRS-P4 (ocean sat) were launched in
1991,1994, 1995 ,1996, 1997 and 1999 respectively.

DIFFERENT STAGES IN REMOTE SENSING
Energy Source or Illumination (A)
Radiation and the Atmosphere (B)
Interaction with the Target (C)
Recording of Energy by the
Sensor (D)
Transmission, Reception, and Processing
(E)
Interpretation and Analysis (F)
Application (G)

Global Positioning SystemGlobal Positioning System
 The Global Positioning System (GPS) is a satellite-basedThe Global Positioning System (GPS) is a satellite-based
navigation system that can be used to locate positionsnavigation system that can be used to locate positions
anywhere on the earth.anywhere on the earth.
• GPS provides continuous (24 hours/day),real-time,GPS provides continuous (24 hours/day),real-time,
3-dimensional positioning, navigation and timing worldwide in3-dimensional positioning, navigation and timing worldwide in
any weather condition.any weather condition.
• GPS was originally intended for military applications, but in theGPS was originally intended for military applications, but in the
1980s, the government made the system available for civilian1980s, the government made the system available for civilian
use.use.
• There are no subscription fees or setup charges to use GPS.There are no subscription fees or setup charges to use GPS.

COMPONENTS OF THE GPS SYSTEM.
The Space Segment The Control Segment The User Segment
Satellites Monitor stations
Master control station
User receivers

SPACE SEGMENT
• The Space Segment of the system consists of the
GPS satellites broadcasting radio signals from
space.
• The GPS operational constellation consists of 24
satellites, including 21 navigational SVs and 3 active
spares orbiting the earth.
• These orbits therefore repeat the same ground
track, as the earth circles beneath them, once each
day.
• There are six orbital planes with nominally four SVs
in each, equally spaced 60° apart.

GPS constellation, indicating the 6 orbital
planes with 4 satellites shown in one orbit.

CONTROL SEGMENT
• The Control Segment consists of a system of
tracking stations located around the world.
• A Master Control station is located at Falcon Air
Force Base, Colorado, USA.
• This Master Control station uploads signal and
clock data to each satellite. The SVs then send
subsets of the orbital signal data to the GPS
receivers comprising the user segment.

USER SEGMENT
• The GPS User Segment consists of the GPS
receivers and the user community. GPS receivers
convert SV signals into position, velocity, and time
estimates.
• Four satellites are required to compute the four
dimensions of X, Y, Z (position) and Time.

GEO-STATISTICS
•Geo-statistics is a branch of applied statistics
developed by George Matheron of the Centre de
Morophologie Mathematicque in Fontainebleau,
France.
•Geo-statistics originated from the mining and
petroleum industries, starting with the work by Danie
Krige in the 1950's and was further developed by
Georges Matheron in the 1960's.
•The original purpose of Geo-statistics centered on
estimating changes in ore grade within a mine.

DEFINITIONS OF GEO-
STATISTICS.
• Establish quantitative measure of spatial correlation to be used
for sub-sequent estimation and simulation. (Deutsch, 2002).
• “Geo-statistics offers a way of describing the spatial continuity
of natural phenomena and provides adaptations of classical
regression techniques to take advantage of this continuity.”
(Isaaks and Srivastava, 1989)
• “Geo-statistics can be regarded as a collection of numerical
techniques that deal with the characterization of spatial
attributes, employing primarily random models in a manner
similar to the way in which time series analysis characterizes
temporal data.”(Olea, 1999)

 Geo-statistics is not tied to assumptions of
population distribution model .
 Geo-statistics incorporates both the statistical
distribution of the sample data and the spatial
correlation among the sample data.

COMBINATIONS OFVARIOUS
DISCIPLINES
mathematicsgeography Databases
Remote
sensing
CAD
computer
software
statistics
cartography Digital
cartography
GEO-
STATISTI
CS

TYPES OF DATA
1. Attribute data:
Says what a feature is
• Eg. statistics, text, images, sound, etc.
2. Spatial data:
Means data which are reffered to earth.
Vector data – discrete features:
• Points
• Lines
• Polygons (zones or areas)
Raster data:
• A continuous surface

What makes data spatial?
PlacenamePlacename
Grid co-ordinateGrid co-ordinate
PostcodePostcode
Distance & bearingDistance & bearing
DescriptionDescription
Latitude /Latitude /
LongitudeLongitude

GISGIS
APPLICATIONAPPLICATION

Agriculture:
Crop waterrequirement
Crop diseases management
Nutrient management
Sustainable agriculture

Contd...
Environment
 management of natural resources
 land, forest, marine, etc.
 monitoring/control of environmental pollution
 environment impact study
Infrastructure
 irrigation management and maintenance
 utility management and maintenance
 electric, water, gas, telephone, etc.

RS IN AGRICULTURE
MANAGEMENT
1. Agro-climatic mapping.
2. Soil mapping.
3. Watershed development.
4. Agricultural drought assessment.
5. Pest assessment and control.
6. Land use/Land cover mapping.

Contd…
7. Crop production forecasting comprises of three
things:
 Identification of crops.
 Acreage estimation.
 Forecasting the yield.

RS IN CRISIS MANAGEMENT
RS helps in planning and
making strategy against the
natural disasters in the
following ways:
Drought monitoring and
assessment.
Flood / cyclone management.
Weather forecasting.

Spatial Correlation:Spatial Correlation:
Cliff and Ord (1973) has defined SC as “ Given aCliff and Ord (1973) has defined SC as “ Given a
group of mutually exclusive units for individuals in agroup of mutually exclusive units for individuals in a
two dimensional plane, if the presence, absence ortwo dimensional plane, if the presence, absence or
degree of a certain characteristics affects thedegree of a certain characteristics affects the
presence, absence or degree of the samepresence, absence or degree of the same
characteristic in neighboring units , then thecharacteristic in neighboring units , then the
phenomenon is said to exhibit spatial correlation”.phenomenon is said to exhibit spatial correlation”.

Cont…
• SC test weather or not the observed values
of a variable at one locality is independent of
values of that variable at neighbouring
localities.
• Here we have two type of correlations
a) positive spatial correlation
b) negative spatial correlation

Classical measures of spatial correlation
If xi and xj are the values of x at ith
and jth
locations
respectively then sc is
Where
(i≠j), wij are the weights such that wij =1, if i and j are
neighbours & 0 otherwise.(

Spatial stratification
“spatial stratification means formation of strata in
such a manner that each stratum consists of units
which are spatially homogeneous”.
SAMPLE SELECTION AND ESTIMATION
PROCEDURES
Consider a population of N areal units
Let
Y- a character under the study
X- auxiliary character
β- a first lag spatial correlation

1) Contigious Unit Based Spatial
sampling (CUBSS)
Let
 Ω(y1 ,y2 ,...,yn ) set of all units in the population
 y1 ,y2 ,...,yn the units drawn at 1st
,2nd
….,nth
draw
respectively
 S1*,S2 *,….,Sn * denote sample set contains units from N
units after 1st
,2nd
,…,nth
draws respectively
 S1*={y1 }, S2*={y1 , y2} ,…,Sn*={y1 , y2 ,…,yn}
 α1,α2 ,…,αn be the probabilities of selection of
y1 , y2 ,…,yn respectively.

Selection of first unit in the sample
 First unit in the sample is selected by SRS
 The probability of selecting ith
unit at first draw will
be 1/N i.e. αi1 = α1 = 1/N
 where i=1,2,….,N
Where αi1 is probability of selecting i
th
unit in first draw.
SELECTION OF SECOND UNIT IN THE SAMPLE:
step 1: select the random number from
1 to N-1(say i)
Step 2: 1 to M (say r), where M is the maximum value of
the auxiliary character.

CONT…
Step 3: select the unit i if (r ≤ Ui2 Xi ) where Ui2 is given as
Ui2 =(1-βd12
)
step 4: reject the unit i and repeat the above process if (r>Ui2 Xi )
The probability of selecting iit
unit in second draw is
where s1
*
is the set of earlier selected units

Selection of subsequent units
For selecting a sample of size n, the above procedure is repeated till n
units are selected with U’i s changing at each draw after selection of
each unit. The general term ui for nth
draw is given as
d1n=1 if 1st
& nth
units selected are 1st
lag neighbor
Thus, for the case of nth
draw

Estimation procedure :
let T1 be the estimator of population mean
Thus T1 is given by
Here T1 is said to be an unbiased estimator of
population mean. Thus the estimate of variance of the
estimator T1 is expressed as

#
2] STRATIFIED CONTIGOUS UNIT BASED
SPATIAL SAMPLING (stratified CUBSS)
Let
 Ωh be the set of all the units in the hth
stratum
 y1h , y2h,….ynh be the values of the unit drawn at first,
second….nth
draw respectively from the hth
stratum.
 L be the total number of strata.
 Here
denote the sample set which contain the units
selected from Nh units
 Let α1h ,α2h ,…..αnh be the probabilities of selection of
y1h, y2h ,…ynh in the hth
stratum respectively
2] STRATIFIED CONTIGOUS UNIT
BASED SPATIAL SAMPLING (stratified
CUBSS)

selection of first unit in the
sample
The first unit in each stratum is selected by
simple random sampling. Clearly, the probability
of selecting ith
unit at first draw in hth
stratum will
be 1/Nh.
αih1 =α1h=1/Nh i=1,2,…..,Nɏ
where αih1 is the probability of selecting ith
unit in
the first draw in the hth
stratum.

SELECTION OF SUBSEQUENT UNITS
Second unit from remaining Nh –1 units is selected from
each stratum using following steps
step1: select a random number from 1 to Nh-1 (say i)
step2: select another number at random from 1 to Mh
(say r), where Mh is the maximum value of the auxiliary
character in the hth
stratum.
step3: select the unit i if (r ≤ Uih2 Xih)
where Uih =(1- ) and Xih be the size measure of the ith
unit in the hth
stratum.

Step 4: reject the unit i and repeat the process if
(r >Uih2 Xih ).
It can be seen that the sum of the
probabilities at the second draw is unity in each
stratum. For selecting a sample of size n, the
above procedure is repeated till nh units are
selected with Ui ‘s changing after selection of
each unit in the stratum.

#
• Thus for the case of nh
th
draw
Estimation procedure:
• An appropriate estimator for the population mean is obtained by
suitably combining the stratum wise estimators of the character
under the study. Let T2 be the estimator of the population mean
obtained by applying stratified CUBSS.
let us define
Where
is the sample mean of hth
stratum,

 T2 is given by
T2 is an unbiased estimator of , an estimate ofȲ
variance of T2 can be written as

3] Modified contiguous unit based spatial
sampling (MCUBSS)
• In this method the first unit is selected by the method of
pps to sampling. It is known that the probability of
selecting any unit by pps is given by Xi /X ,
such that clearly the probability of selecting ith
unit at the
first draw will be αi1 = αi= Xi/X i=1,2,…,N whereɏ αi1
is the probability of selecting ith
unit in the first draw.

Contd...
Estimation procedure:
Here the unbiased estimator of the population mean
obtained by modified CUBSS technique is given as
The estimate of variance of the estimator T3 is given as

• In this method the population is divided into homogeneous
strata on the basis of spatial correlation or the administrative
boundaries are considered as strata. Sample is then selected
from each stratum using modified CUBSS technique.
• The unbiased estimator of population mean denoted by T4
An estimate of variance of

The study was conducted in Rohtak district of
Haryana to estimate the irrigated area in the
district.
Y: The irrigated area ,has been treated as
character
X: Total cultivated area, has been taken as the
auxiliary character (its highly correlated with the
character )
CASECASE
STUDYSTUDY

DATA USED
1]Two sets of data were used for
study
a] Spatial data
b] Attribute data
2]The data was procured from
District hand book of census
(DHC) of Rhotak of the year
1991.
3]There were 492 villages in the
district (polygon map with
each unique ID no)
4]File format
AAT PAT
DBF

• Spatial correlation was computed
• The value of overall spatial
correlation was 0.41
• Also the spatial stratification was
done since the data was highly
correlated the entire map came
out to be a single stratum.

Sample selection and estimation
 One thousand samples of different sample sizes
30,50,75,100 were selected using the proposed
sampling procedure .
Beside the proposed estimators T1, T2 , T3 and T4
corresponding to the sampling technique
CUBSS, stratified CUBSS, Modified CUBSS ,
Stratified modified CUBSS respectively. The
estimators of traditional sampling techniques
were selected as T5 , T6, T7 , T8 ,T9

CRITERIA FOR COMPARISON OF
DIFFERENT ESTIMATORS
 To compare the performance of the proposed sampling
scheme with the various existing sampling schemes
 The percentage relative bias (RB),relative efficiency (RE), as
compared to the estimator based on SRSWOR and
coefficient of variation (CV) has been calculated using the
following formulas
 percent relative bias :
RB =(Ti - Ȳ)/ *100Ȳ
where Ti is the sample mean for ith
estimator ; i=1,2,3,…..9 and is the population meanȲ

#
• RELATIVE EFFICIENCY: RE for the estimator Ti
(i=1,2,….9) as compared to the estimator T6 is given
by
RE=v(T6)/v(Ti)
where V(T6) is the variance of the estimator (T6) based
on SRSWOR and V(Ti) is the variance of the
estimator Ti for i=1,2,3,4,5,7,8,9.
Coefficient of variance:
CV=(√v(Ti)/Ti )*100

 The results clearly indicate that the percent relative bias is
very low ranges from 0.003 to 0.74.
 Relative efficiency : There is observed that there is
remarkable gain in efficiency for all the proposed estimators
as compared to the traditional estimators.
 Among the proposed estimators T4 is most efficient than the
other T3 , T2 , and T1
 Coefficient of variation of proposed sampling (T1 ,T2, T3 and
T4 ) ranges from 2.28 to 6.37 where as in proposed
estimators (T5 ,T6 T7, T8 and T9) it ranges from 5.95 to 14.25
 Thus it indicate that proposed estimators are more stable than
traditional estimators.

• Managing Spatial Variability which is Helpful Precision farming.
• Precision farming essential for serving dual purpose of
enhancing productivity and reducing ecological degradation.
• The Precision Agriculture model using geoinformatics
technology for India while addressing ecological integrity
issues would provide an innovative route for sustainable
agriculture in globalised and liberalized economy.

REFERENCESREFERENCES
Prachi Misra Sahoo, Randhir Singh and Anil Rai(2006),Spatial Sampling
Procedures for Agricultural Surveys using Geographical Information
System. J. Ind. Soc. Agril. Statist. 60(2): 134-143
Rabi n Sahoo (2006), Geostatistics in Geoinformatics for Managing Spatial
Variability. Indian Agricultural Research Institute, pusa, New Delhi .
K.Elangovan (2006), GIS Fundamentals, Applications and Implementations
M.Anju Reddy (1999), Remote Sensing and Geographical Information System,
B.S Publications Hyderabad

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