Int. J. Agric.Sc & Vet.Med. 2015
Arvind Singh Tomar, 2015
ISSN 2320-3730 www.ijasvm.com
Vol. 3, No. 1, February 2015
© 2015 www.ijasvm.com. All Rights Reserved
Research Paper
RELATIONSHIP BETWEEN RAINFALL AMOUNT,
MEAN DAILY RAINFALL INTENSITY AND RAINY
DAYS AT UDHAM SINGH NAGAR DISTRICT,
UTTARAKHAND, INDIA
Arvind Singh Tomar1*
*Corresponding Author: Arvind Singh Tomar,  [email protected]
In the present study, long-term daily rainfall data (1962-2012) of Udham Singh Nagardistrict was
analysed to understand relationships between Rainfall Amount (RA), Mean Daily Rainfall Intensity
(MDRI) and Rain Days (RD) on monthly, seasonal and annual basis. The study revealed erratic
distribution of rainfall occurrence as MDRI with highly correlated values (0.83-0.90) was observed
for different months, seasons and annual data series. The value of X* (percent rain amount
cumulated in first 50% of rain days) was found highest (11.89%) for March, whereas, among
seasons, its highest value (10.45%) was observed for season S2 (March-May). In the same
way, value of first 50% rainfall cumulated (Y*) was found highest for October month and among
seasons with season S4 (October-December). It was also found that 29.59% rain days per
annum accounted for 78.98% rainsreceived at Udham Singh Nagar district.
Keywords: Rainfall amount, Normalized rainfall curve
INTRODUCTION
characteristics and its variation at different levels
at a place into consideration. One of the most
important problems in hydrology deals with
interpreting a past record of hydrologic events in
terms of furnishing valuable information for future
use. In this study, association between cumulated
percentage rain amount (X) and cumulated
percentage rain days (Y) has been examined to
study relationship of rainfall amount with rain
events on monthly, seasonal and annual basis
Themost vital and critical input for agricultural
productionis rainfall and in Indian conditions, its
distribution is very erratic and varies from region
to region and year to year. It is a well known fact
that a few rain events with large rain amounts
contribute to bulk of monthly, seasonal and annual
rainfall. As crop yields depend on amount and
distribution pattern of rainfall to a great extent,
therefore, it is a matter of interest to study rainfall
1
Department of Irrigation & Drainage Engineering, College of Technology, G.B. Pant University of Agriculture & Technology,
Pantnagar 263145, Uttarakhand, India.
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Int. J. Agric.Sc & Vet.Med. 2015
Arvind Singh Tomar, 2015
by drawing Normalized Rainfall Curves (NRCs)
as relationship between these two, i.e., “X” and
“Y” are best described in exponential terms
(Ananthkrishnan and Soman, 1989). The earliest
representation of association between rain
amount and rain days was given by Olascoaga
(1950) for climatic zones of Argentina in the form,
x = ayebx, where “x” is cumulated percentage
rain amount, “y” is cumulated percentage rain
days and “a” and “b” are empirical constantas
with some definite values. They found that a single
NRC gave satisfactory representation of rainfall
with a variety of rainfall regimes.
collected from Meteorological observatory
situated at Crop Research Centre of G.B. Pant
University of Agriculture & Technology, Pantnagar
and rain amount measuring greater than or equal
to 0.10 mm was only considered for data series
which is then sorted in ascending order for different
months, seasons and years.In this study, available
daily rainfall data has been examined for all 12
months of year individually;four Indian seasons
{S 1 (January-February); S 2 (March-May); S 3
(June-September); and S4 (October-December)};
and year as a whole. The available daily rainfall
data has been examined and studied with the help
of graphical representation between cumulated
percentage rain amount (X) and cumulated
percentage rain days (Y), prepared by
progressive cumulating daily rainfall values after
arranging series in ascending order for abovesepecified periods individually.
Onthe basis of daily rainfall distribution in North
and Central America for a period of 30 years,
Martin (1964) found that single NRC could
represent with a good degree of accuracy and
regarded it as a “universal daily rainfall distribution
curve”. Similarly, Ananthkrishnan and Rajan
(1987) examined analytical representation of
NRCs and concluded that representation of rainfall
series of different rainfall regimes is dependent
on some measures of dispersion while De-sousa
and De-Silva (1998) studied precipitation
normalized curve by an analytical method to
measure maximum probable rainfall intensity by
using NRC for five stations at Brazil and obtained
good results in all cases and stressed that
estimates for maximum probable rainfall intensity
are reliable and may be used in planning of small
hydraulic projects. Tomar and Ranade (2001) also
studied association of rainfall amount with rain
events on the basis of 20 years of daily rainfall
data and concluded that 21.23% rainfall was
available in 71.04% rain days during monsson
season at Indore region of Madhya Pradesh.
To understand it clearly, considering the month
of January for ‘P’ number of years; total number
of days will be 31P out of which if ‘N’ days have
recorded measurable amount of rain (> 0.1 mm),
then after excluding rainless days, N < 31P, daily
rainfall values were arranged in ascending order.
Total rain recorded in N days (R) and Mean Daily
Rainfall Intensity (MDRI) is then calculated by R/
N where, R = r1 + r2 + r3 + … + … + rN. Rainfall for
first ‘k’ days (Rk) of ordered series is given by
relation, Rk = r1 + r2 + r3 + … + … + rk and
cumulated percentage rain amount (X) for ‘k’ days
is calculated by Xk= (100 * Rk)/R, whereas,
cumulated percentage rain days (Y) for ‘k’ days
are calculated byusing equation,
Yk = (100 * k)/N
It has been found that as ‘k’ takes values
from 0 to N, Xk and Yk takes values from 0 to
100. By plotting corresponding values of Xk and
Yk, NRC for given period can be obtained in the
MATERIALS AND METHODS
The long-term daily rainfall data for 51 years (19622012) of Udham Singh Nagar district was
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51
Int. J. Agric.Sc & Vet.Med. 2015
Arvind Singh Tomar, 2015
similarity between them and hence, they will be
represented bysame NRC. With larger values of
CV of rainfall series, greater deviation is observed.
Previous studies have shown that NRC of
stations with vastly different rainfall regimes is
practically identical if CV values of rainfall series
are close to one another.
Figure 1: Illustration of a Normalized
Rainfall Curve (NRC)
RESULTS AND DISCUSSION
Thefindings of analysis of rainfall data series for
Udham Singh Nagardistrict on the basis of NRCs
drawn for different months, seasons and annual
rainfall series is presented in Table 1. The
uniformity of rainfall distribution is assessed by
two methods, firstly, by using common measures
of dispersion (e.g., mean, standard deviation,
coefficient of variation and correlation coefficient)
and secondly, by analyzing duration of rain days
for the first 50% of rain amount to happen (Y*)
and rain amount which occurred in first 50% of
rain days (X*).
shape of graph for exponential functionas
shown in Figure 1.
By following same procedure and utilizing
daily values of seasonal and annual rainfall for
total period of 51 years, NRCs for different
seasons and annual basis were also drawn.
On NRC, two points (X*, 50) and (50, Y*) are
of interest where X* is percentage rain amount
cumulated in first 50% of rain days and Y* is
percentage number of rain days in which first 50
percentof precipitation is cumulated. Since NRC
is directly related to Coefficient of Variation (CV),
cumulated percentage number of rain days,
which contribute 50% rain amount in ordered
rainfall series (calculated from zero end of NRC),
is directly related to CV of rainfall series under
consideration.
From corresponding approximate values for
all months, seasonsand years, it is clear that
maximium skewedness (or non-uniformity) is
found in the month of November while March was
found with minimum skewedness. In case of
seasonal rainfall, skewedness is maximum in
season S4 (October-December) and minimum
in season S2 (March-May). From Table, it is evident
that CV is found lowest in the month of June
(121.25%) while its largest value was observed
in October (172.42%) during the study period.
Similarly, lowest CV value was observed for
season S3 (June-September), and its largest
value was found in season S 4 (OctoberDecember).
The CV of rainfall on rain days is an important
statistical parameter and uniquely determines
important properties of daily rainfall distribution. It
is an established fact that if two rainfall series
have same CV values, then ratio of their mean
daily rainfall will be equal to ratio of their Standard
Deviation (SD). When two such normalized
series are arranged in ascending order, there is
Deviation from mean was found maximum for
monthof September (35.95%) and minimum for
November (7.39%). Data was found to be highly
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Int. J. Agric.Sc & Vet.Med. 2015
Arvind Singh Tomar, 2015
Table 1: Statistical Analysis and Approximate Values of X* and Y* on Monthly, Seasonsal
and Annual Rainfall Bais at Udham Singh Nagar District
Period (s)
CV
SD
MDRI
Corr. Coeff.
R
N
D
N' = N/51
X*
Y*
January
130.87
12.79
9.77
0.87
1387.60
142
1581
2.78
9.25
86.62
February
145.95
13.77
9.43
0.87
1754.70
186
1467
3.65
8.42
87.63
March
124.78
7.48
6.00
0.90
893.50
149
1581
2.92
11.89
85.91
April
154.13
11.15
7.23
0.86
788.30
109
1530
2.14
9.12
89.91
May
129.41
13.70
10.59
0.89
2329.60
220
1581
4.31
10.99
86.82
June
121.25
23.39
19.29
0.89
9298.00
482
1530
9.45
10.15
84.65
July
129.84
31.95
24.60
0.87
22144.10
900
1581
17.65
8.19
86.44
August
138.53
33.01
23.83
0.87
21614.30
907
1581
17.78
8.03
87.54
September
145.87
35.95
24.64
0.85
13431.20
545
1530
10.69
6.74
88.62
October
172.42
32.30
18.73
0.85
2135.40
114
1581
2.24
7.69
91.23
November
139.55
7.39
5.29
0.83
206.40
39
1530
0.76
5.91
87.18
December
148.60
13.67
9.20
0.87
607.00
66
1581
1.29
7.41
86.36
Season S1
(Jan-Feb)
139.19
13.33
9.58
0.87
3142.30
328
3048
6.43
8.78
87.20
Season S2
(Mar-May)
138.99
11.66
8.39
0.88
4011.40
478
4692
9.37
10.45
87.66
Season S3
(Jun-Sept)
135.94
31.89
23.46
0.87
66487.60
2834
6222
55.57
8.12
87.30
Season S4
(Oct-Dec)
187.57
25.26
13.46
0.85
2948.80
219
4590
4.29
6.10
91.78
Annual
(Jan-Dec)
147.06
30.01
19.85
0.86
76590.10
3859
18654
75.67
7.48
88.55
Note: CV = Coefficient of Variation (%); SD = Standard Deviation (mm); MDRI = Mean Daily Rainfall Intensity (mm); Corr. Coeff. =
Correlation Coefficient; R = total rainfall (mm); N = total number of rain days; D = total number of days in period (No.); N’ = mean
number of rain days per annum (No.); X* = percent rain amount cumulated in first 50% rain days; and Y* = percent rain days in which
first 50% rains is cumulated.
correlated as correlation coefficient for all months,
seasons and yearswerefound positive i.e. with
increase of one variable, another variable
increases and was found good with values in the
range of 0.83-0.90. As far as rainy days are
concerned, November is found with lowest (39)
rainy days, followed by December (66), and
October (114), whereas, highest number of rainy
days were observed in August (907) followed by
July (900), and September (545).
mm) and August (23.83 mm) while November had
its minimum value (5.29 mm) followed by March
(6.00 mm) and April (7.23 mm). Season S3 (JuneSeptember) was found to have maximum MDRI
(23.46 mm), whereas, season S2 (March-May)
observed minimum MDRI value as 8.39 mm. The
variation of SD and MDRI and CV and number of
rain days on monthly, seasonal and annual basis
are shown in Figures 2 and 3 respectively.
It is a well known fact that a few number of
rain events with large rain amounts contribute to
bulk of monthly, seasonal and annual rainfall. Data
The MDRI values were found highest in
September (24.64 mm), followed by July (24.60
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Int. J. Agric.Sc & Vet.Med. 2015
Arvind Singh Tomar, 2015
days (with rainfall more than MDRI) accounted
for 80.04% rainfall, whereas, for February, 131
days contributed for 407.00 mm rains. In
percentage form, 70.43% rain days collectively
captured 23.19% precipitation at Udham Singh
Nagar district.
Figure 2: Monthly, Seasonal and Annual
Variation of SD and MDRI
Similarly, 104, 81, 151, 317, 609, 623, 385, 86,
27, 46 and 2717 days contributed to 242.70 mm,
196.50 mm, 572.00 mm, 2049.30 mm, 4567.70
mm, 4510.00 mm, 2708.80 mm, 508.80 mm,
35.40 mm, and 132.10 mm rainfall for March, April,
May, June, July, August, September, October,
November, and December respectively. In the
same way, it was also observed that 69.80, 74.31,
68.64, 65.77, 67.67, 68.69, 70.64, 75.44, 69.23
and 69.70% rain days accumulated 27.16, 24.93,
24.55, 22.04, 20.63, 20.87, 20.17, 23.83, 17.15
and 21.76% rainsduring months of March, April,
May, June, July, August, September, October,
November, and December respectively.
Figure 3: Monthly, Seasonal and Annual
Variation of CV and Number of Rain Days
From analysis of daily rainfall data series of
59 or 60 days for season S1 (January-February),
it was found that 225 days contributed 684.00 mm
rainswhich is equivalent as 68.60% rain days
amounted for 21.77% rainfall or in other words,
31.40% rain days with rainfall greater than MDRI
accounted for 78.23% rainfall. From the analysis
of basic datasetconsisting of daily rainfall values
of 92 days (March-May, season S2) of 51 years, it
was found that 334 days contributed for 959.30
mm rainfall, whereas, in percentage form,
69.87% rain days amounted for 23.91% rainfall.
In other words, it can be said that in 30.13% rain
days (with rains greater than MDRI), 76.09%
rainfall was accumulated during season S2.
regarding seasons was analyzed to obtain
contribution of significant rainfall days, i.e., rain
days amount not less than MDRI with idea to
calculate percentage of significant rainfall days
and amount contributed by them on monthly,
seasonal and annual basis. With days having rain
less than MDRI and cumulative rainfall on these
days taken into account for different months,
seasons and years, it was found thatin January,
94 days contributed for 277.00 mm rainfall. In
percentage form, 66.20% rain days amounted for
19.96% rainfall and in other words, 33.80% rain
In Indian context, knowledge of rainfall
occurring during June to September months is
extremely important for optimizing crop production
as Indian subcontinent gets its 75% rainfall during
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54
Int. J. Agric.Sc & Vet.Med. 2015
Arvind Singh Tomar, 2015
South-West monsoon season, therefore, from the
analysis of basic datasetof season S 3 (JuneSeptember) consisting of 122 days, it was found
that 1922 number of days contributed for
13503.10 mm rainfall which can also be
interpreted in the form that 20.31% rainfall was
accumulated in 67.82% rain days. In other words,
during season S3 (June-September), 79.69%
rainfall occurred in 32.18% rain days with rainfall
greater than MDRI.
Table 2: Trendline Equations of NRCs
on Monthly, Seasonal and Annual Basis
for Udham Singh Nagar District
Trend Line Equation
Coefficient of
Determination
January
y = 14.202 ln(x) + 23.485
0.908
February
y = 14.105 ln(x) + 25.286
0.929
March
y = 14.942 ln(x) + 19.102
0.905
April
y = 14.720 ln(x) + 23.833
0.929
May
y = 14.306 ln(x) + 21.782
0.893
June
y = 12.960 ln(x) + 26.220
0.892
July
y = 12.600 ln(x) + 29.262
0.906
August
y = 12.555 ln(x) + 29.537
0.898
September
y = 12.456 ln(x) + 31.715
0.917
October
y = 13.106 ln(x) + 30.370
0.923
November
y = 15.627 ln(x) + 24.325
0.983
December
y = 13.861 ln(x) + 26.858
0.934
Season S1
(Jan-Feb)
y = 13.960 ln(x) + 24.968
0.916
Season S2
(Mar-May)
y = 14.202 ln(x) + 22.976
0.899
Season S3
(Jun-Sept)
y = 12.508 ln(x) + 29.620
0.899
Season S4
(Oct-Dec)
y = 13.144 ln(x) + 31.340
0.934
Annual
(Jan-Dec)
y = 12.705 ln(x) + 30.022
0.905
Period (s)
The analysis of daily dataset consisting of
rainfall values of 91 days for season S4 (OctoberDecember) revealed that 164 days has
contributed 681.50 mm rains. In percentage form,
74.89% rain days amounted for 23.11% rainfall
or in other words, 25.11% rain days (with rainfall
greater than MDRI) accounted for 76.89% rainfall,
whereas, daily rainfall valuebasic dataset of 365
or 366 days (January-December) of each year
for the study period (1961-2011) showed that 2717
days contributed for 16098.60 mm rainfall. In
percentage form, 70.41% rain days amounted for
21.02% rainfall and in other words, 29.59% rain
days (with rains greater than MDRI) accounted
for 78.98% rainfall.
In this study, relationship between rain days
and rain amount by nearest logarithmic
trendlinehas been presented and is expressed in
the form of a logarithmic equation,
Figure 4: Monthly, Seasonal and Annual
Variation of X* and Y*
y = a ln(x) + b where “x” is cumulative percentage
rain amount, “y” is cumulative percentage rain
days and “a” and “b” are constants having
different values for different months, seasons and
annual rainfall series. The respective equations
of good fit trendlinesof NRCs for different months,
seasons and annual rainfall series are presented
in Table 2.
The values of X* and Y* effectively help in
determining nature of rainfall uniformity as well
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Int. J. Agric.Sc & Vet.Med. 2015
Arvind Singh Tomar, 2015
as its skewedness as in July, first 50% of rain
days accounted for only 8.19% rainfall amount
while last 13.56% rain days yielded 50.00% of
monthly total, which shows highly skewed nature
of rainfall. The monthly, seasonal and annual
variation of X* and Y* during study period is shown
in Figure 4.
highest (11.89%) for March, whereas, its
highest value (10.45%) was observed for
season S2 (March-May) and for annual series,
it was found as 7.48%.
• The value of percent rain days in which first
50% rainfall is cumulated (Y*) was found
highest for October (91.23%), among
seasons (S4, October-December) as 91.78%
and for annual series it was observed as
88.55%.
CONCLUSION
In this study, long-term daily rainfall data of 51
years (1962-2012) was used to study rainfall
variation with the help of statistical parametersto
establish association between rainfall amount,
mean rainfall intensity, and rain daysfor Udham
Singh Nagardistrict on monthly, seasonal and
annual basis with the help of NRCs. From
foregoing study, following conclusions may be
drawn:
• For season S1 (January-February), 31.40%
rain days cumulated 78.23% rainfall, whereas,
during season S2 (March-May), 76.09% rainfall
accumulated in 30.13% rain days. In case of
season S3 (June-September), 32.18% rain
days accounted for 79.69% of rainfall while for
season S4 (October-December), 25.11% rain
days accounted 76.89% rainfall.
• The CV is found to be highest for October
(172.42%), whereas, for season S4 (OctoberDecember) and annual series, it was 187.57%
and 147.06% respectively.
• For annual rainfall data series (JanuaryDecember), 29.59% rain days with rainfall
greater than MDRI accounted for 78.98%
rainfall.
• The SD is found to highest for September
(35.95 mm), whereas, for season S3 (JuneSeptember) and annual series, it was obtained
as 31.89 mm and 30.01 mm respectively.
REFERENCES
1. Ananthakrishnan R and Rajan C K (1987),
“Analysis of Representation Systems for
Daily Rainfall Data and Determination of
Common NRC”, Ind. J. Climato., Vol. 7,
p. 355.
• The value of MDRI in case of different months
varies in the range of 5.29-24.64 mm,
whereas, their seasonal variation was
observed in the range of 8.39-23.46 mm and
it was 19.49 mm for annual data series with
highly correlated values in the range of 0.830.90.
2. Ananthakrishnan R and Soman M K (1989),
“Statistical Distribution of Daily Rainfall and
its Association with Coefficient of Variation
of Rainfall Series”, Intl. J. Climato., Vol. 9,
pp. 485-500.
• Mean number of rain days for months varied
in the range of 0.76-17.78, whereas, on
seasonal basis, they varied in between 4.29
and 55.57 with 75.67 days on annual basis.
3. De-Sousa S and De-Silva R (1998), “Intensity
Rainfall Analysis by Precipitation Normalized
Curve”, Intl. J. Meteoro. and Climate.,
pp. 319-323.
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cumulated in first 50% of rain days) was found
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6. Rai Sircar N C (1955), “Some Aspects of
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