

PRINT VERSION MODULE


Module Objective 


Introduction 


Statistical Terms/Parameters often used
in Frequency Analysis 



Dispersion Characteristics 





Which value/data
qualifies as an annual peak of a year?


How to Ensure Fitness of data for Frequency
Analysis? 




Empirical
Vs. Theoretical Distribution Curve 


Plotting Position 


Which Distribution fits well? 


Case Study 


Confidence Bands and Confidence Limits



Expected Probability 


How to perform DIndex test 


Outliers 


Handling Diverse Scenarios 


References 



Contributor 



Acknowledgement 






MODULE
OBJECTIVES 





 To get familiarized with a few Statistical
parameters
 To grasp difference between empirical
vs. theoretical frequency distribution
 To understand & perform various
tests to ensure fitness of data for flood frequency analysis
 To learn how to plot confidence band
and its significance
 To grasp the meaning and significance
of confidence band; confidence limit; outliers; expected probability
etc.







INTRODUCTION 





The previous module on this topic provides
elementary knowledge of flood frequency analysis. This module moves
a step further, and enables the reader to handle complex problems
related to this topic.
Estimates of extreme events of given
recurrence interval are used for a host of purposes, such as design
of dams, coffer dams, bridges, floodplain delineation, flood control
projects, barrages, and also to determine impact of encroachment
of flood plain etc. Frequency analysis, if done manually, is burdensome,
tedious, and leaves little manoeuvring space if something wrong
is noticed at the end of calculation. It often requires calculations
all over again. Accordingly, this module attempts at presenting
some statistical parameters, its application in flood frequency
analysis, and thereafter introduces HECSSP software that offers
multiple functions to perform frequency analysis speedily and accurately.







STATISTICAL
TERMS/PARAMETERS OFTEN USED IN FREQUENCY ANALYSIS 




Statistics 





Statistics is
concerned with the collection, ordering and analysis of data. Data
consists of sets of recorded observations or values. It also provides
criteria for judging the reliability of the correlation between variables;
means for deriving the best relationship for predicting the one variable
from known values of other variables. Any quantity that can have a
number of values is a variable. A value that a variable takes is called
'Variate'. A variable can be either;
 Discrete  a variable, whose possible
values can be counted, e.g. number of rainfall days in a month
or year. Number would take only integer values within zero and
infinity, or
 Continuous  a variable; which can
take on any value within specified interval. Annual maximum discharge,
for example, is a continuous variable as it could be any value
between zero and infinity.







Sample
and Population 





Any time set of
recorded or observed data does not constitute the entire population.
It is simply a fraction of entire population and is called a 'sample'.
By deducing the characteristics exhibited by sample, inferences are
drawn about the nature of entire population. In other words, collected
samples help us predict the likely magnitude and occurrence of future
events. It is obvious here that quality and length of sample used
in analysis hugely impact the quality of forecast of ensuing events. 










Measure
of central tendency 





The arithmetic mean of a set of 'n' observations
is their average:
When calculating from a
frequency distribution, this becomes:
In MS excel, for a given
set of data, the mean can be determined by entering function 'average(a1:a20)'
in formula bar. Here, a1:a20 indicates the range of cells
from a1 to a20 containing sample data, if sample length is 20.
Mean is not a firm or fixed value; and
fluctuates within a range with variation in length of samples. The
range of this fluctuation is better expressed by another statistical
parameter, i.e. Standard Error of Mean. Other measures of
central tendency are median and mode.







Dispersion
Characteristics 




Range 





The mean, mode
and median give important information about the central tendency of
data but they do not tell anything about the spread or dispersion
of samples about the centre.
For example, let us consider the two
sets of data:
26, 27, 28, 29 30, and 5, 19, 20, 36,
60
The simplest measure of dispersion is
the range  the difference between the highest and the lowest values.
For these two set of data, both samples have a mean of 28, but range
for first set is 4, for second it is 55. Obviously, one is clearly
more tightly arranged about the mean than the other.







Standard
Deviation 





The standard deviation, SD is most widely
used measure of dispersion around Mean. It indicates the slope of
distributed curve on either side of the mean. According to the nature
of dispersal of data, slope could be either gentle or steep. A high
SD indicates gentle slope, widely scattered around mean and higher
range; while, converse is true, when SD is less. Based on this description,
it can be presumed that first set of data will have smaller SD than
that of the second set. A normally distributed curve slopes alike
on either side of the mean as shown here. This aside, for normally
distributed data, mean, median and mode, all coincide.
The variance of a set of
data is the average of the square of the difference in value of
a datum from the mean:
This has the disadvantage
of being measured in the square of the units of the data. The standard
deviation is the square root of the variance:
This formula with denominator
'n' indicates SD of entire population. However, for all practical
purposes, we deal with 'samples' only, and in such case, denominator
'n' is replaced by (n1) to account for limited length of data.
Excel formula to estimate this parameter is =stdev(Range
of data). Here, for two sets of data, SD computed is 1.58
& 21 respectively, which is consistent with our presumption
made earlier.







Skewness 





In several cases, frequency of occurrence
of variables is not normally distributed and plots either skewed
+ve (right) (as shown in the fig.) or skewed ve (left). In other
words, slopes of the curve on either side are dissimilar. Unlike
normally distributed data, mean, median and mode for skewed data
do not coincide. Peaked point of skewed plot is the location of
mode. For normally distributed curve, skewness is zero.
This parameter is determined
by function skew(range of data) in
MS Excel. It is evident, from table, that for evenly distributed
data set, skewness is zero. Second set of data is positively skewed.
HECSSP software itself
computes these parameters and performs a number of tasks using them.







WHICH
VALUE/DATA QUALIFIES AS AN ANNUAL PEAK OF A YEAR ? 





Collection of a set of particular type
of data is purpose driven. For frequency analysis of flood peaks
corresponding to a return period of 50yr or so, we look for collection
of a set of instantaneous peak discharge of different years. Here,
instantaneous peak discharge of a year means that discharge is highest
of all discharge values flowed past a measuring section during the
period. The question is how to gather this set of information. Following
Para discusses this aspect.









Hourly discharge observation is not only
expensive but also impracticable. Instead, a widely prevalent practice
in India is to record discharge observation once a day (usually
at 0800hr or so), and water level every hour. It is important to
note that recorded discharge observation may or may not be the peak
discharge of the day; and therefore, it can't be a true representative
of an instantaneous peak discharge of a day. Let us understand it
differently. In a plot shown here, water level hydrograph and the
level when discharge was carried out have been shown together. It
is easily noticeable here that peak water level (hence discharge)
occurred between two observations. This means that if we pick up
instantaneous peak discharge out of observed discharge recorded
in a year, missing out true instantaneous peak can't be ruled out.
Therefore, it had better look for all such peaks in a year, and
pick up a corresponding discharge value that is highest of all.
Followings are few approaches suggested to consider before finalizing
an array of annual peaks.
1. Fit a rating curve (s) between observed
discharge and corresponding water level. Rating curves so developed
and hourly water level hydrograph together can be used to obtain
a nobreak/continuous discharge series of a particular year. A plot
of water level and continuous discharge series, developed using
HYMOS software, is displayed here. Peak of this series represents
instantaneous annual peak of that year.









2. In absence of rating curve, a correlation
between past observed discharge or mean daily discharge (maximum
of a year) and instantaneous peak discharge can be developed. This
relationship can be used to generate peak discharge corresponding
to maximum observed discharge for subsequent years.
(for detailed discussion, pl refer to Hydrologic
Frequency Analysis, Vol3 published by US Army Corps of Engineers
1975, http://www.hec.usace.army.mil/publications/IHDVolumes/IHD3.pdf
)
3. In some quarters, peak daily or peak
mean daily discharge data are raised by certain percentage, say
20 or 30%. This method is little ambiguous and subjective as all
peak daily values may or may not touch instantaneous peak by application
of a certain percentage.







HOW
TO ENSURE FITNESS OF DATA FOR FREQUENCY ANALYSIS? 





Annual peaks gathered for
frequency analysis must be a product of random factors only. Presence
of one or more data influenced by manual and/or systematic errors
gravely distorts the distribution of plot and its reliability, if
go unnoticed in the analysis. So, it is essential that a suspected
data should be detected and treated for its modification or retention
or deletion before analysis. This apart, data should possess attributes,
such as homogeneity, randomness, and stationarity. These attributes
are explained in succeeding paragraphs.




a.

Homogeneity
Homogeneity implies that the sample is
representative of same population. The homogeneous requirement means
that each flood occurs under more or less similar conditions. Two
flood events are homogeneous, if both are caused by same factor,
such as rainfall. Flood peaks triggered by dam break, breach in
embankment are isolated events, and should not be part of peaks
created by rainfall. It is assumed that though peak flows of finite
years' have been recorded; the same type of 'Statistical Character'
(mean, standard deviation, and skewness) was always there and would
behave alike in future too. For this reason, a set of data belonging
to same population must closely exhibit the similar statistical
behaviour with another set of data of same population. To test homogeneity
of data, Student 't' test is normally performed.




b.

Independence/Randomness
This is explained in previous module
on this topic. Independence or randomness is usually investigated
by Turning Point test.




c.

Stationarity
In this the properties or characteristics
of the sample do not fluctuate with time. Linear trend test determines
this property of sample.
If any of these is not an attribute
of a sample, the use of probability/theoretical frequency distribution
may lead to erroneous results. Accordingly, it is desirable that
before any analysis, one must see that sample should conform to
these attributes.
HECSSP offers no tools to perform these
tests. Nevertheless, interested users, can use HYMOS software to
test if compiled set of data qualifies for flood frequency analysis.
For more details, we recommend reference to Hydrology ProjectI
Training Module no.43. This material is available as part of this
week's module.







EMPIRICAL
Vs. THEPRETICAL DISTRIBUTION CURVE 





Absolute frequency  Supposing there
is a variable which can take values from 0 to 100. A sample of this
variable holds 50 different values. Let us group these data in five
equal intervals, e.g., 020, 2040,  , 80100. There distribution
across five groups is 'absolute frequency'. Absolute frequency,
say n divided by N, is relative frequency or probability. Please
notice that sum total of relative frequency is '1'. This concept
is used a little later.













A relative frequency curve plotted on
the basis of distribution of data in a sample presents a distribution
curve known as empirical distribution curve. This distribution and
its statistical parameters help an engineer fit a theoretical frequency
distribution curve, as closely to the empirical distribution as
possible to ensure mathematical tractability further.







Fig 1






As understood a while ago, the probability
or relative frequency is defined as the number of occurrences of
a variate divided by the total number of occurrences, and is usually
designated by P(x). The total probability for all variates should
be equal to unity, that is, SP(x) = 1.
Distribution of probabilities of all variates is called Probability
Distribution, and is usually denoted as f(x) as shown in
Fig.1.
The cumulative probability curve, F(x)
is of the type as shown in Fig.2.



Fig 2






The cumulative probability or 'probability
of nonexceedance', designated as P(x < x), represents
the probability that the random variable has a value less than certain
assigned value x. Additive inverse of P(x < x),
or P(x > x), is termed
as Exceedance Probability. Reciprocal of exceedance probability
is return 100 times the Exceedance Probability is called as Exceedance
Frequency. Now, glance at Table1; and read what the probability
of 60 not getting exceeded is.



Table 1







In the context of flood frequency analysis,
we apply above concepts by assuming the instantaneous yearly flood
peaks as the variate 'x'. Then, if the functions f(x) or
F(x) becomes known by fitting a theoretical distribution,
it is possible to find out the probability (or return period) of
a flood peak, or conversely, a flood magnitude of desired return
period (also return interval or recurrence interval).
There are a number of probability distribution
functions f(x), which have been suggested by statisticians.
HECSSP supports following distribution functions.
(Reader can download and install HECSSP software from site,
http://www.hec.usace.army.mil/software/hecssp/downloads.html
)








Without log transformation

I. Normal &


II. Pearson type
III 
With log transformation

I. Log normal
& 

II. Log Pearson
type III 
Another often used distribution is Gumbel
method. Even if, HECSSP software does not include this method,
user can readily use mean and standard deviation to estimate flood
peak corresponding to a return period, T = (1/P) by use of formula
placed below:
X_{T}
= M + B * (l_{n} (l_{n} (1P)))
Where,

M = X_{mean}
 0.45005 * Standard Deviation 

B = 0.7797 * Standard
Deviation 
However, this method is recommended
when length of data is fairly large, say more than 100 (ref: Patra
K C, Hydrology and Water Resources Engineering). Alternatively,
when data is scarce, i.e., data length is below 100, user may use
Gumbel table, which features in almost every hydrology book, to
read K, frequency factor for given sample size and return period.
In this case, X_{T }is estimated by
X_{T}=
X_{mean} + K * St Deviation







PLOTTING
POSITION 





To assign a probability to a sample data
(also called variate) and to determine its 'plotting position' on
probability sheet, sample data consisting of N values is arranged
in descending order. Each data (say the event X) of the ordered
list is then assigned a rank 'm' starting with 1 for the highest
up to N for the lowest of the order. The exceedance probability
of a certain value x is estimated by formula presented below:
p
= (ma)/(Nab+1)
Where, m is rank of the sample data in
the array; N represents the size of sample; and 'a' and 'b' are
constants. For different methods, a and b assume different values.
For Weibull method, a & b equal zero; and hence, P reduces to
m/(n+1). HECSSP, by default, uses Weibull method to show dispersion
of data. Nevertheless, option is available for alternate methods
by defining appropriate value of a & b. Of these, the Weibull
formula is most commonly used, because it is simple and intuitively
easily understood to determine the probability. (For detailed discussion
on the choice of a particular method, reader may refer to Applied
Hydrology by Ven T Chow, p  ).







WHICH DISTRIBUTION FITS WELL ? 





HECSSP offers graphical plot displaying
scatter of sample data in addition to computed curve. Here, user
has choice to choose method of plotting position and a theoretical
curve of his choice. Graphical plot is a visual aid of determining
worthiness of choice broadly; and therefore, conclusion based on
merely eye judgment is hugely subjective. To overcome this limitation,
user can analyze the result distilled by software and employ any
one of the following tests to measure the strength of fitness. However,
such analysis needs to be done outside; as HECSSP contains no builtin
function of this kind. This module presents steps to perform Dtest
only. Details with regard to others, users may refer to Hydrology
Project Training Module no.43.













 Chisquare test
 KolmogorovSmirnov test
 Binomial goodness of fit test, and
 Dindex test
Once a particular distribution is found
the best, it is adopted for calculation of peak floods in future.
Dindex is calculated by
Dindex =
S1to6 (abs(Xi_{observed}  Xi_{computed})/(mean
of sample)
where,

Xi _{observed}=
observed value of a given p, exceedance probability 

Xi _{computed}
= for identical p, value determined by distribution curve 
Dindex test is shown later in this module.







CASE
STUDY 





This point forward, a real sample (Table
2) has been collected for its frequency analysis with HECSSP
software. The application of the method of plotting and
fitting a theoretical distribution curve, analysis of output will
help reader grasp the functions of this software speedily. The software
outputs a series of additional information, which have been discussed
at appropriate locations.













Step 1
As quoted earlier, this set of data is
required to be investigated to confirm its adherence to desired
attributes of sample data, i.e. homogeneity, randomness and stationarity.
Following is screenshot of HYMOS software which is used to conduct
series homogeneity test of a given series. A popup window in the
middle of this screenshot indicates results of this series as 'accepted'.
In all three tests, hypothesis, that series is random, is not rejected.
This implies that the current sample is a collection of random data.












Step
2
Subsequent steps begin with creation
and saving of an EXCEL sheet with two columns  first for year and
second for discharge. This file is imported (Fig.4) in HECSSP software
to carry out frequency analysis. Interested reader is suggested
to go through 'User's Manual' of this software (p 47 to p 49 to
learn how to import data from MS excel), which is available under
'Help' menu of software.
This manual is also available at http://www.hec.usace.army.mil/software/hecssp/documentation/HECSSP_20_Users_Manual.pdf
.
Optionally, user can directly input data
by selecting 'Manual' button on 'Data Importer' window (Fig.4).
To open 'Data importer' window, click on 'Data' menu followed by
choosing 'New'.



Fig 4



Step
3
Once, data is available, Chapter 6 of
'User's Manual' help user finish frequency analysis. 'General Frequency
Analysis Editor' window as shown in Fig.5 can be activated by selecting
Analysis New  General Frequency Analysis option on the menu.
An analysis report (Table 3) along with distribution curve (Fig.6)
generated by the software for this set of data using Log Pearson
type III distribution is placed next. Before, we delve into results;
let us familiarize ourselves with a couple of lines appearing on
the plot. Later, we will discuss their significance, and how they
are estimated.



Tiny circular points in blue are annual
peaks occupying their position on the plot (also probability sheet)
according to probability assigned to them by 'Weibull method'. As
discussed earlier in the module, this scattering is 'Empirical Frequency
Distribution'. A line in red denotes Log Pearson TypeIII 'Theoretical
Distribution Curve'. Could you read on the plot what return period
for circular point farthest to the right is? It is roughly 30yrs.
If we desire to ascertain peak discharge of still higher return
period sticking to empirical distribution, no information is available.
For a majority of hydrological and hydraulic related studies, flood
magnitude of return period of 50 yrs or more is needed. Such estimations
are extracted with the help of theoretical distribution plot, which
is mathematically extended further.



Fig 5



 A dotted line in blue is expected
probability curve. This aspect is discussed later.
 A pair of two lines in green on either
side of plot is 90% confidence band. This aspect is also covered
later.






Table 3









Of several useful
contents generated by software, two of them need special attentions.
These are:

I. Confidence Limits,
and 

II. Expected Probability 







CONFIDENCE
BANDS AND CONFIDENCE LIMITS 





The record of
annual peak flow at a site is a random sample collected over a period
of time. A varied nature of causative factors and complex interactions
among them bring about randomness in the sample. Therefore, in all
likelihood, a different set of samples of same population results
in different estimate of the frequency curve. Thus, an estimated flood
frequency curve can be only an approximation to the true frequency
curve of the population of annual flood peaks. To gauge the accuracy
of this approximation, one may construct an interval or a range of
hypothetical frequency curves that, with a high degree of confidence,
contains the population frequency curve. Such intervals are called
confidence intervals and their end points are called confidence limits.
This is analogous to standard error of mean or standard error of mean
relationship concept. 





The two limits of 0.05 and 0.95, or 5%
and 95% chance exceedance curve,(pl see the result in table 3),
imply that there is 90% chance/probability that discharge value
will lie/occur between these bounds; and only 10% of observation
may fall outside this band. If we put it differently, upper limit
suggests a flow with 5% of exceedance probability, or (10095),
i.e. 5% non exceedance probability. If certainty of this degree
is warranted for any project, flow of this magnitude can be chosen
for design, but at the cost of escalation in project cost. In fact,
this choice is a tradeoff between cost of the project and safety
of the structure. Similar conclusion can be drawn about lower limit
The confidence band width is determined
by a formula given below:
Q_{U,L} = Q_{mean}
± K_{U,L} * St Deviation
Where,
K_{U,L} is a function of exceedance
probability, sample size, skewness coefficient and confidence interval
opted by the user. The value of K_{U,L} declines with rise
in sample size. This brings two lines representing QU & QL closer
to each other, and therefore, a narrower band will appear. HECSSP
assumes exceedance probability of 0.05 and 0.95 by default and returns
the output. User, at his discretion, can select any other value
instead. For more details about K_{U, L}, reader may refer
to 'Reference 2'.











EXPECTED
PROBABILITY 





The expected probability
adjustment is necessitated to account for a bias introduced in the
distribution curve on account of shortness of data. Factually, all
distributions assume spread of data from  8
to + 8; while in reality, this is far from
real. This calls for measures to address short length of data. Table
4 is an excerpt from Applied Hydrology by Ven Te Chow listing
correction factors for different return periods. 





Where, N is number
of sample data used in the analysis. Please notice that as N approaches
infinity, expected probability equals exceedance probability. Here
too, HECSSP offers both alternatives to compute or not to compute
expected probability and corresponding flood values for various exceedance
probabilities (Fig.7). 









HOW
TO PERFORM DINDEX TEST 





HECSSP software, by default, outputs
flood peaks of a few exceedance frequencies like 0.2, 0.5, 1.0,
2.0, 5.0, 10.0, 20.0, 50.0, 80.0, 90.0, 95.0, and 99.0. However,
appropriate part of window, shown at Fig.8, can be suitably adjusted
by the user to gather flood peaks of desired exceedance frequency,
usually matching with what tabulated by the software using Weibull
method. (pl refer to tabular result under Table 3).













An attempt to
compute Dindex values for this set of data, outside the HECSSP environment,
is placed at Table 5. Please mark that data, as highlighted in red
in Table 3, populate this table for calculation of Dtest. It could
be seen, lower the value of Dtest, the better the fit is.












OUTLIERS 





Outliers are values in a data set which
plot significantly away from remainder of sample data (main body
of the plot), and their deletion, retention and modification warrants
prudent considerations of all of the factors giving birth to them.
In Paragraph to follow, this aspect has been discussed at length.
The following equation is used to detect outliers:
Q_{High},
Q_{Low} = Q_{mean} ± K_{N} * St Deviation
Where,

K_{N} is a frequency
factor and varies according to sample size. 
HECSSP automatically performs detection
process; reports and analyzes the set of data accordingly.







HANDLING
DIVERSE SCENARIOS 





The study covered
in this module plots all annual peaks more or less closely aligned
to theoretical distribution line (see Fig.6). It also means the absence
of even a single peaks straying from rest of peaks. So, the number
of outlier for this case is zero. Nevertheless, samples not as coherent
as cited here are always a possibility; and it is likely that they
may contain outliers  both high and low or either of the two; i.e.
zero flows; or even historical floods outside the systematic (also
continuous) records of annual peaks.
In dealing with such records, one, however,
must be convinced about the authenticity of data, and should guard
against entries of all inflated or dubious values in the analysis.
In HECSSP, presence of zero flows and
low outliers are automatically detected and counted out by the software,
and a conditional probability adjustment, to account for truncated
values, is employed to estimate revised plotting position. Software
also modifies values of statistical parameters to define theoretical
distribution curve.






In a deviation
from above, high outliers, so long as they are not suspected values,
are not eliminated from the record as they are invaluable piece of
the flow record and might be representative of longer period of record.
For example, a flood value in a set of data, detected by software
as outlier, could be the largest flood that has ever occurred in an
extended period of time backward. Like other cases, HECSSP detects
high outlier as well, and presents the analysis accounting for revised
length of time period entered by user and number of high outliers
detected by software itself. A computed curve returned by the software
utilizes modified statistical parameters, i.e. mean, standard deviation,
and skewness coefficient. Fig.9 is one of the windows of the software
that lets user make appropriate entry to define Historical Period,
if a high outlier falls beyond the systematic record. To gather more
information about mathematical steps involved in dealing with varying
cases such as cited here, interested users should refer to material
referenced against Sl. No. 2, at the end of this chapter.
Here, we place sample data set (Table
6 & 7) for Flood Frequency Analysis under different conditions.
User may key in this set of data in HECSSP to perform frequency
analysis for different cases.














As outlined in
one of the preceding paragraphs, HECSSP has the ability to detect
low outliers and/or zero flows and projecting the probability curve
by introducing conditional probability adjustment. Contrary to this,
analysis of high outliers and historical data do need a few entries
by user. Fig.10 deals with high outliers, where a peak discharge
of 71,500 cumec is labeled as a high outlier by software, and an entry
of 1892 by user in a cell by start year implies this peak is highest
known value since year 1892. Fig.11 deals with historical data;
where user has entered historical flood value along with corresponding
year. An entry of 1974 against end year signifies no significant flood
since regular discharge recording ceased in year 1955. 
























REFERENCES 





 HECSSP User's Manual,
available at http://www.hec.usace.army.mil/software/hecssp/documentation/HECSSP_20_Users_Manual.pdf
 Guidelines for Determining
Flood Flow Frequency Bulletin 17B of the Hydrology SubCommittee
 A publication by US Department of the Interior Geological Survey
Office of Water Data Coordination, http://water.usgs.gov/osw/bulletin17b/bulletin_17B.html
 Ven Te Chow, David
R Maidment, Larry W Mays, (International Edition 1988), Applied
Hydrology, McGrawHill Book Company
 Patra, K C, (2001),
Hydrology & Water Resources Engineering, Narosa Publishing
House
 Hydrologic Frequency
Analysis, Vol3 published by US Army Corps of Engineers 1975,
http://www.hec.usace.army.mil/publications/IHDVolumes/IHD3.pdf
 Mutreja, K N, Applied
Hydrology, Tata McGraw Hill Publishing Company Limited, N Delhi
 Hydrology Project
Phase I (India), Training Module no.43







CONTRIBUTOR 

Anup
Kumar Srivastava 


Director 



National
Water Academy, Pune, India 










ACKNOWLEDGEMENT 

Author of
this module hereby acknowledges the invaluable support received from
Shri D S Chaskar, and Dr R N Sankhua, both Directors, National Water
Academy, CWC, Pune in preparation and presentation of this module
in current shape.












