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This
study was under taken in the U.G. thesis work in the Dept. Of SWCE, CAET, OUAT,
Bhubaneswar during the year 201819. Puri district has latitude of 20°50'40''N and a longitude of
85°09'04''E. The average rainfall at Puri district is around 1673.9 mm, though
it receives high amount rainfall but most of the rainfall occurred during khari. So most of the crops get low
yield due to improper crop planning. Thus, this study is proposed to be
undertaken with the following objective: Probability analysis of annual,
seasonal and monthly rainfall data of Puri district. So rainfall data were
collected from OUAT, Agril Meteorology Department from 2001 to 2017 (17 years)
monthly, seasonal and annual rainfall were analysed .Probability analysis have
been made and equations were fitted to different distributions and best fitted
equations were tested. Monthly, Annual and seasonal probability analysis
of rainfall data shows the probability rainfall distribution of Puri district
in different months, years and seasons. It is observed that rainfall
during June to Sep is slightly less than
1000 mm and cropping pattern like paddy (110 days) may be followed by mustard
is suitable to this region. Also if the kharif
rain can be harvested and it can be reused for another rabi crop by using sprinkler or drip irrigation, which will give
benefit to the farmers. Annual rainfall of Puri district is
1264.4 mm at 50% probability level.
Keywords: Rainfall, Probability analysis, Crop
planning, Command area, Hirakud
INTRODUCTION
Puri district
has latitude of 20°50'40''N and a longitude of 85°09'04''E. The average
rainfall at Puri district is around 1673.9 mm, most of the rainfall occurred
during kharif. Thus, this study is
proposed to be undertaken with the following objective: Probability analysis of
annual, seasonal and monthly rainfall data of Puri district.
Thom [1] employed mixed gamma probability
distribution for describing skewed rainfall data and employed approximate
solution to nonlinear equations obtained by differentiating log likelihood
function with respect to the parameters of the distribution. Subsequently, this
methodology along with variance ratio test as a goodnessoffit has been widely
employed [24] applied incomplete gamma probability distribution for rainfall
analysis. In addition to gamma probability distribution, other twoparameter
probability distributions (normal, lognormal, Weibull, smallest and largest
extreme value) and threeparameter probability distributions (lognormal,
gamma, loglogistic and Weibull) have been widely used for studying flood
frequency, drought analysis and rainfall probability analysis [4].
Gumbel [5] and Chow [6] have applied gamma distribution
with two and three parameter, Pearson typeIII, extreme value, binomial and
Poisson distribution to hydrological data.
MATERIALS AND
METHODS
The data were collected from District
Collector’s Office, Puri for this study.
Rainfall data for17 years from 2001 to 2017 are collected for the presented
study to make rainfall forecasting through different methods.
Probability distribution functions
For seasonal rainfall analysis of Puri
district, three seasons kharif (JuneSeptember), rabi (October
to January) and summer (February to May) are considered.
The data is fed into the Excel spreadsheet,
where it is arranged in a chronological order and the Weibull plotting position
formula
is then applied.
The Weibull plotting
p = m/N+1
where m=rank number
N=number of years
The recurrence interval is given by:
T = 1/p = N+1/m
The values are then subjected to various
probability distribution functions namely normal, lognormal (2parameter),
lognormal (3parameter), gamma, generalized extreme value, Weibull,
generalized Pareto distribution, Pearson, logPearson typeIII and Gumbel
distribution. Some of the probability distribution functions are described as
follows:
Normal distribution:
The probability
density is:
p (x) = (1/σ √2π) e^{(xµ)2/2σ2}
where x is the variate, µ is the mean
value of variate
p( x ≤ ) = 1 / σ√2π _{∞}∫^{x}
e –(x^{ }µ)^{2/}2σ^{2} dx
This represents the area under the curve
between the variates of ∞ and x.
Lognormal
(2parameter) distribution: The probability density is:
p(x) = (1/ σ_{y }e^{y}√2 π) e ^{–(y}^{ µ}_{y}^{)2/}^{2}^{σy}
where y =ln x, where x
is the variate, µ_{y} is the mean of y and σ_{y} is the
standard deviation of y.
Lognormal
(3parameter) distribution: A random variable X is said to have threeparameter lognormal
probability distribution if its probability density function (pdf) is given by:
^{f(x)}{1/(x λ) σ√2 π * exp {1/2(log(x λ) µ / σ)^{2}}, λ < x < ∞, µ > 0, σ > 0}
0, otherwise
Where µ, σ and λ are known as location, scale
and threshold parameters, respectively.
Pearson distribution:
The general and
basic equation to define the probability density of a Pearson distribution:
p(x) = e _{∞}∫^{x }a+x / b^{0} + b_{1}x +b_{2}x^{2 }* dx
Where a, b_{0}, b_{1} and b_{2}
are constants.
The criteria for determining types of
distribution are β_{1}, β_{2} and k where
β_{1} = µ_{3}^{2 }/ µ_{2}^{3}
β_{2} = µ_{4}^{ }/ µ_{2}^{2}
k = β_{1 }(β_{}1 + 3)^{2 }/ 4 (4 β_{2 } 3β_{1})(_{ }2 β_{2 } 3β_{1} – 6)
Where µ_{2}, µ_{3} and µ_{4}
are second, third and fourth moments about the mean.
LogPearson type III
distribution: In
this the variate is first transformed into logarithmic form (base 10) and the
transformed data is then analyzed. If X is the variate of a random
hydrologic series, then the series of Z variates where
z = log x
are first obtained. For this z series, for any recurrence interval T and the coefficient of skew C_{s}
σ_{z}=standard deviation of the Z
variate sample
= √∑ (z  z)^{2} / (N – 1)
And C_{s}=coefficient of skew of
variate Z
= N ∑(z  z)^{3} / (N – 1) (N – 2)σ_{z}^{3 }* σ
N=sample size=number of years of record
Generalized Pareto distribution: The family of generalized Pareto
distributions (GPD) has three parameters µ, σ and ξ.
The cumulative distribution function is
F _{(ϵ, µ, σ)} (x) = { 1 (1 + ξ(xµ) / σ)^{1/ξ} for ξ ≠0 }
{ 1 exp ( xµ / σ) for ξ = 0 }
For x > µ when ξ > 0 and x < µ when ξ < 0, where
The probability density function is
f _{(}_{ξ, µ, σ)} (x) = 1/ σ ( 1 + ξ (x  µ) / σ ) ^{(1 / ξ – 1)}
Or
f _{(}_{ξ, µ, σ)} (x) = σ ^{1/ ξ}/ (σ + ξ (x  µ)) ^{(1 / ξ + 1)}
again, for x > µ and x < µ  σ/ξ when ξ<0
RESULTS AND
DISCUSSION
The various parameters like mean, standard
deviation, RMSE value, were obtained and noted for different distributions. For
generalized extreme value and generalized Pareto distribution the other
parameters like shape parameter ξ, scale parameter σ and location parameter µ are
also noted for further calculation. Similar procedure is followed for the
seasonal, annual and pentad analysis. The rainfall at 90%, 75%, 50%, 25% and
10% probability levels are determined. The distribution “best” fitted to the
data is noted down in a tabulated form in Table
1 [710].
In
the present study, the parameters of distribution for the different
distributions have been estimated by FLOODflood frequency analysis software.
The rainfall data is the input to the software programme. The best fitted
distribution of different month and season and annual were presented in Table 1. The annual rainfall in 50%
probability was found to be 1673.9 mm for Puri district of Odisha [1114].
During Kharif at 50% probability
level, the rainfall is 1220.68 mm whereas only 242.92 mm and 26.43 mm was
received during rabi and summer respectively, so water harvesting
structures may be made to grow crops during rabi
and summer to utilise the water from
the water harvesting structures to increase the cropping intensity of the area.
It is also observed that at 75% probability level the June, July, August and
September received more than 100 mm, so farmers of these area can grow crops in
upland areas suitably paddy can be grown followed by any rabi crop in rabi season
like mustard or kulthi in upland areas. In Figure
1, the plot between different months and amount of rainfall in different
probabilities were shown, It is observed that July month gets highest amount of
rainfall compared to other months [1517].
CONCLUSION
Forecasting of rainfall is essential for
proper planning of crop production. About 70% of cultivable land of Odisha
depends on rainfall for crop production. Prediction of rainfall in advance
helps to accomplish the agricultural operations in time. It can be concluded
that, excess runoff should be harvested for irrigating postmonsoon crops. It
becomes highly necessary to provide the farmers with highyielding variety of
crops and such varieties which require less water and are earlymaturing in
Puri district of Hirakud command area of Odisha. It is also observed that at
75% probability level the June, July, August and September received more than
100 mm, so farmers of these area can grow crops in upland areas suitably paddy
can be grown followed by any rabi crop in rabi
season like mustard or kulthi in upland areas. Annual rainfall of
Puri district is 1673.9 mm at 50% probability level. It is observed that July month gets highest
amount of rainfall compared to other months [18].
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