 Open Access
 Total Downloads : 23
 Authors : Sunil Poudel, N. K. Goel
 Paper ID : IJERTCONV3IS03034
 Volume & Issue : ETWQQM – 2014 (Volume 3 – Issue 03)
 Published (First Online): 24042018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Investigations of Nonstationarity on Hydrological Data of Koshi Basin, Nepal
Sunil Poudel
Department of Hydrology Indian Institute of Technology Roorkee
Roorkee, India
N. K. Goel
Department of Hydrology Indian Institute of Technology Roorkee
Roorkee, India
Abstract – Hydrological designs are based on the premise that past data are representative of future and the statistical parameters of the data are stationary in nature. Many a times past data may not be representative of future and hence it becomes necessary to check assumption of stationarity of data. Further it is essential to assess the implications of this assumption on design floods and water availability estimates. Nonstationarity of 21 stations hydrological data of the Koshi river basin are analysed. Data on many stations show nonstationarity. It is found from analysis of extreme annual discharge data of 21 stations in Koshi basin that 4 stations have short term dependence and 8 stations have long term dependence. Four stations have both short term and long term dependence. Similarly 13 stations show no trend and 4 stations show negative trend, 2 stations shows positive trend and results obtained are different in different tests on 2 stations, however overall trend obtained in both station is negative. Nonmonsoon runoff from 7 stations show the short term dependence, 9 stations show long term dependence and 5 stations show both long term and short term dependency. Similarly for monsoon runoff, 6 stations show short term dependence, 5 stations show long term dependence and 4 stations show both long term and short term dependence. For annual runoff, 7 stations show short dependence, 6 stations show long term dependence and 4 stations show both long term and short term dependence. In the trend analysis of 21 stations most of the stations show no trend in annual and seasonal runoff. One station shows negative trend in nonmonsoon runoff and 4 stations show positive trend in nonmonsoon runoff. While in the case of monsoon runoff 4 stations show negative trend and 1 station shows positive trend. Three stations of annual runoff show negative trend and only one station shows positive trend.
Keywords: Stationarity, nonstationarity, dependence, trend, autocorrelation

INTRODUCTION
Hydrological time series show nonstationarity due to numbers of reasons. Land use/cover change, construction of
models to optimize water systems. Climate change is the prominent cause for the nonstationarity in hydrological time series. Hirsh, (2010) had discussed on a perspective of nonstationarity and water management. He discussed on issue of nonstationarity due to climate change as a concerned topic to the water management community. Long term and short term dependence and trend are used for the determination of the nonstationarity. Lye, et al. (1994) studied the long term dependence in annual peak flows of Canadian rivers. They used parametric and non parametric approaches for the investigation of short term and long term dependence of the time series. The serial correlation structure of 90 Canadian rivers was analysed. Ceschia, et al. (1994) had made study trend analysis of mean monthly maximum and minimum surface temperatures of the 19511990 period in Friuli Venezia Giulia. The behaviour of seasonal and yearly average of the monthly means of maximum and minimum daily surface temperature, covering the period 195190, in some stations of the Italian Hydrographic Service spread over the region of FriuliVenezia Giulia has been analysed by the Spearman test with the aim of determining a possible trend.
In this paper 21 series extreme annual discharge and 21 series of average annual, monsoon and nonmonsoon runoffs from Koshi basin, Nepal are investigated for the identification of nonstationarity.

METHODOLOGY

Investigation Of Short Term Dependence

Turning Point Test (Kendalls test) ( Kendall and Stuart, 1976)
1
1
Kendalls test is based on a binary series. If xi1 < xi > xi+1 or xi1 > xi < xi+1, then xi is assigned the value 1, otherwise, it is assumed to be zero. The number of ones, m, is approximately normally distributed for sample size n.
dam upstream of the measurement site, change in climate etc.
2
16n 29 2
are some of the reasons of nonstationarity. A note on Stationarity and Nonstationarity, WMO (2012) discussed about stationarity and non stationarity, causes of nonstationarity, distinguishing stationary and nonstationary
m N
3
n 2, 90
(1)
series, and practical application of nonstationary time series data. Stationarity and nonstationarity has great implication on the water resource management. Milly, et. al (2008) mentioned that stationary is dead due to anthropogenic causes so we need to find ways to identify nonstationary probabilistic models of relevant environmental variables and to use those

Rank Von Neumann Ratio Test (Madannsky, 1988)
Let r1,……, rn denote the ranks associated with the xi values. The rank Von Neumann ratio is given by following formula for sample size n.
n
n
ri
ri1
cannot exceed 1.0. The Hurst coefficient is only the measurement available for long term dependence.
2
2
v i2
n(n2 1) / 12
For large n, v is approximately distributed as
(2)
To check the assumption of using normally distributed data for testing Hursts K, the nonparametric bootstrap approach (Effron 1979) was used.
To test longterm dependence of a series, following
20 12
procedure is adopted:
N2,
(3)

Annual flow series x
x ,……..,x
are assumed as
5n 7
1, 2 n
independent observ s. Each x has the same


Von Neumann Ratio Test (Madannsky, 1988)
(x x )
(x x )
n
2
t t1
ation i
probability of occurrence, 1/n.

Uniform random data i between one and n are generated, then x is chosen as one point in the bootstrap sample.
Let v t2
(4)
i
This is repeated ntime to generate a bootstrap
t
t
n 2
step
x x
t1
If data are independent, v is approximately normally distributed with E(v) = 2 and
Var (v) = 4 (n – 2)/(n2 1)
sample of the same size n as that of original sample.

Hursts K is calculated for the bootstrap samples.

Steps (ii) and (iii) are repeated for a large number of times (10,000 times in this study).

Number of times that observed K value of the sample
is exceeded by the 10,000 bootstrapped K values is
Z (v 2) /[4(n 2) /(n2 1)]1/ 2


Autocorrelation Test (Yevjevich, 1971)
(5)
counted.

P value is calculated
P value No. of K Kobs.
(10)
For a sample of size n, the lagone autocorrelation, r1, is calculated as and r1 is normally distributed as follows for sample size of n.
10,000
If value of P is less than the value at specified significance level, it is concluded that the sample has long term dependence at that level of significance. Otherwise, it
n x
y _
has no longterm dependence.
_
_
i
x i y
r
r
i1
1
<>(6)

Identification Of The Trend In Data Series
n _ 2 n
_ 2
xi x . yi y
i1
1
i1
1
n 3 3n 2 4 2
Trend in the time series data has been identified using Mann Kendall test, Spearmans Rho test and TheilSens
r1 N n ,
n 2 n 2 1
(7)
slope estimator.

MannKendall Test (Mann, 1945: Kendall, 1975)




Investigation Of Long Term Dependence

Hurst K Test (Hurst, 1951)
Hurst coefficient is the measure of long term dependence. The Hurst coefficient is estimated by
The MannKendall test is based on the test statistics S defined as follows:
n1 n
Hursts K as K has a lower variance than other estimators currently in use. Calculation of Hursts K is simple and
S= sgn (x j xi )
i1 j i1
(11)
straight forward which is given by
logR / S
Where the xj and xiare the sequential data values, n is the length of the data set and
K logn / 2
(8)
Sgn ()= 1 if >0
=0 if =0
Where R is range of cumulative departures from the mean.
=1 if <0
Mann (1945) and Kendall (1975) have documented that
n
n
i.e. R Max. x Min. n x
when n8, the statistic S is approximately normally
i x
i1
i
i1
x (9)
distributed with mean and the variance as follows:
where xi
i th variate
E(S)=0
n
x mean of
the sample
V(S)= [n(n 1)(2n 5)
ti (i 1)(2i 5)]/18
i1
(12)
s = standard deviation
ti is the number of ties to the extent of i.
n = sample length.
K is theoretically 0.5 for series of independent data; it
ZMK
= 1
> 0 , ZMK=
+1
< 0 and
(13)
increases, when there is greater degree of dependence and ZMK= 0 if S=0

Spearmans Rho test (Sneyers, 1990) Let given sample data set {xi ,i=1,2.n}
monsoon period and remaining November to May are considered as nonmonsoon period.
Analysis of the long term and short term dependence of
n
n
2
2
D=1 6[R(xi i)]
i1
/[n(n2
1)]
(14)
annual and seasonal runoffs has been made and presented in Table 3.
From the dependence analysis it has been found that
R (xi) is the rank of the ith observation xi in the sample of size n. As per Sneyers, 1990)
E(D)=0
nonmonsoon runoff of 7 stations show the short term dependence, 9 stations show long term dependence and 5 stations show both long term and short term dependence.
Similarly for monsoon runoff 6 numbers of data stations
V(D)=
1
(n 1)
D
Z=
V (D)
(15)
show short term dependence, 5 stations show long term dependence and 4 stations show both long term and short term dependence. In case of annual runoff 7 stations show short dependence, 6 stations show long term dependence and

TheilSens Slope Estimator (Theil, 1950; Sen,
1968)
It has been called "the most popular nonparametric technique for estimating a linear trend". This non parametric statistic calculates the magnitude of any significant trends found. The Sen slope estimator (Sen, 1968) is calculated as follows:
4 stations show both long term and short term dependence.
Trend analysis has also been made for all the average annual, monsoon and nonmonsoon runoff. The summary of the result obtained from trend analysis has been presented in Table 4.
Out of 21 stations most of stations show no trend in annual and seasonal runoff. One station shows negative trend
For j=1n
Q (xij xkj )
(i k)
1 k i nj
(16)
in nonmonsoon runoff and 4 stations show positive trend in nonmonsoon runoff. While in the case of monsoon runoff 4 stations show negative trend and 1 station shows positive trend. Three stations of annual runoff show negative trend and only one station shows positive trend. Three stations
The slope estimate is the median of all Q values.

RESULTS
To detect the nonstationarity different statistical tests for short term and long term dependence have been carried out including trend detection tests in the data series. These tests have been applied for the 95% confidence level.

Analysis of the Instantaneous Peak Annual Discharge There are 21 stations at different rivers on Koshi basin in
Nepal whose annual instantaneous peak discharges are available. Those data are investigated for the short term and long term dependence. The results are shown in Table 1.
Out of 21 stations data, 4 stations have short term dependence and 8 stations have long term dependence. Four stations have both short term and long term dependence.
Trend in the given extreme annual discharge is also calculated. The summary of the trend analysis is shown in Table 2.
In the trend analysis 13 stations out of 21 stations show no trend and 4 station show negative trend. Two stations shows positive trend. In 2 stations different results are obtained from the different tests for the significance level of 5%. However the overall trend in these two stations is also negative.

Analysis of the Average Annual and Seasonal Runoff Average monthly runoff (Million Cubic MeterMCM) is
calculated for each station from available average monthly discharge. Month of June to October are considered as
show different result in different tests but nature of the trend is same in both tests.
Table 1. Summary of test statistics and dependence of Annual peak discharge
No
Station No.
Data Length (Year)
Turning Point Test
Rank Von Neuman Ratio Test
Von Neuman Ratio Test
Auto Correlation Test
Short term Dependence
Hurst Coefficient (K)
Generated Sample (K)
Long term persistence
600.1
22
0.35
1.58
0.56
0.73
No
0.65
0.65
No
602
30
0.60
0.56
0.18
0.32
No
0.71
0.64
No
602.5
25
0.33
1.10
0.78
0.75
No
0.73
0.65
No
604.5
32
1.30
0.27
0.49
0.46
No
0.63
0.64
No
606
21
2.53
1.47
1.66
1.62
No
0.84
0.66
Yes
610
35
1.24
1.22
0.92
0.80
No
0.65
0.63
No
620
42
0.12
0.27
0.39
0.39
No
0.79
0.63
Yes
627.5
17
0.00
1.36
0.02
0.21
No
0.63
0.65
630
42
1.60
2.34
2.07
2.07
Yes
0.74
0.63
Yes
640
24
1.17
1.20
0.02
0.17
No
0.72
0.65
No
647
33
0.14
2.01
1.88
2.03
Yes
0.82
0.64
Yes
650
41
1.14
3.30
0.41
0.53
No
0.73
0.63
Yes
652
22
1.89
1.14
0.57
0.71
No
0.76
0.64
Yes
660
22
0.68
0.33
0.41
0.37
No
0.69
0.63
No
668.5
20
0.56
2.03
2.36
2.60
Yes
0.91
0.65
Yes
670
22
1.23
1.88
0.20
0.04
No
0.71
0.63
No
680
20
0.50
0.72
1.19
1.11
No
0.65
0.67
No
681
16
0.42
0.53
0.12
0.07
No
0.76
0.66
No
684
11
0.00
0.93
0.36
0.37
No
0.69
0.67
No
690
22
3.24
2.55
2.40
2.47
Yes
0.78
0.63
Yes
695
22
1.36
1.25
0.02
0.16
No
0.61
0.64
No
Table 2. Summary of test statistics and trend status of Annual Peak discharge
Station No.
Data Length (Year)
Mann Kendall test
Spearmans Rho test
TheilSen's Slope Estimate (Q)
Remarks on Trend
600.1
22
0.0283
0.0052
0.000
No Trend
602
30
2.9644
2.8286
5.273
Negative Trend
602.5
25
2.0797
2.3138
0.929
Negative Trend
604.5
32
0.0649
0.0602
1.450
No Trend
606
21
2.2668
2.2709
108.000
Negative Trend
610
35
0.4408
0.3046
1.500
No Trend
620
42
1.6479
1.5187
7.407
No Trend
627.5
17
0.6596
0.5931
0.523
No Trend
630
42
2.4182
2.2426
18.000
Negative Trend
640
24
1.9111
2.2269
0.925
Different result
647
33
2.9911
3.1404
14.514
Positive Trend
650
41
0.0225
0.5118
0.000
No Trend
652
22
0.4361
0.5947
94.615
No Trend
660
22
0.5181
0.4165
1.938
No Trend
668.5
20
2.9864
2.789
3.178
Positive Trend
670
22
1.0996
1.6065
3.333
No Trend
680
20
0.7543
0.4175
1.389
No Trend
681
16
0.4052
0.4556
22.000
No Trend
684
11
1.796
2.113
146.667
Different result
690
22
1.7237
1.8004
6.471
No Trend
695
22
0.9759
0.8902
86.667
No Trend
Table 3. Summary of test statistics and dependence of Annual and Seasonal runoff
Station No./Data Length (Yr)
Description
Turning Point Test
Rank Von Neuman Ratio Test
Von Neuman Ratio Test
Auto Correlatio n Test
Short term Dependence
Hurst Coefficient (K)
Generate d Sample (K)
Long term persiste nce
600.1/19
Nonmonsoon Runoff
0.76
2.96
3.35
3.40
Yes
0.90
0.66
Yes
Monsoon Runoff
0.76
3.05
3.30
3.34
Yes
0.89
0.66
Yes
Annual Runoff
0.76
2.96
3.35
3.40
Yes
0.90
0.66
Yes
602/24
Nonmonsoon Runoff
1.34
0.92
0.65
0.77
No
0.69
0.65
No
Monsoon Runoff
1.34
0.95
0.91
1.05
No
0.70
0.65
No
Annual Runoff
1.34
0.92
0.65
0.77
No
0.69
0.65
No
602.5/22
Nonmonsoon Runoff
0.18
1.37
1.51
1.45
No
0.82
0.65
Yes
Monsoon Runoff
0.18
2.11
2.66
1.74
No
0.71
/td>
0.65
No
Annual Runoff
0.18
1.91
1.77
1.00
No
0.69
0.65
No
604.5/30
Nonmonsoon Runoff
0.74
3.25
3.17
3.21
No
0.82
0.64
Yes
Monsoon Runoff
1.49
0.81
0.69
0.79
No
0.78
0.64
Yes
Annual Runoff
1.49
0.94
0.99
1.14
No
0.82
0.64
Yes
606/20
Nonmonsoon Runoff
1.67
0.98
1.45
1.03
No
0.74
0.65
No
Monsoon Runoff
1.67
2.35
2.25
2.07
No
0.89
0.66
Yes
Annual Runoff
2.22
1.92
1.91
1.72
No
0.85
0.66
Yes
610/33
Nonmonsoon Runoff
1.56
2.09
0.72
0.89
No
0.78
0.63
Yes
Monsoon Runoff
0.28
0.19
0.15
0.07
No
0.70
0.64
No
Annual Runoff
0.14
0.40
0.34
0.43
No
0.75
0.64
No
620/42
Nonmonsoon Runoff
1.75
3.40
2.92
2.85
Yes
0.77
0.63
Yes
Monsoon Runoff
1.00
3.57
2.88
2.98
Yes
0.72
0.63
No
Annual Runoff
1.00
3.95
3.23
3.30
Yes
0.74
0.63
No
627.5/15
Nonmonsoon Runoff
0.44
0.22
0.21
0.46
No
0.78
0.67
No
Monsoon Runoff
0.44
1.34
0.11
0.30
No
0.64
0.66
No
Annual Runoff
0.44
1.34
0.01
0.17
No
0.63
0.66
No
630/37
Nonmonsoon Runoff
0.53
1.96
1.42
1.44
No
0.75
0.64
No
Monsoon Runoff
0.13
2.83
2.90
2.84
Yes
0.89
0.63
Yes
Annual Runoff
0.27
2.65
2.61
2.65
Yes
0.90
0.63
Yes
640/22
Nonmonsoon Runoff
0.18
2.45
2.25
2.43
Yes
0.64
0.65
No
Monsoon Runoff
1.41
0.50
0.58
0.45
Yes
0.62
0.66
No
Annual Runoff
1.41
0.16
0.07
0.12
Yes
0.64
0.66
No
647/29
Nonmonsoon Runoff
1.82
1.97
1.51
1.62
No
0.77
0.64
No
Monsoon Runoff
0.45
1.02
0.74
0.64
No
0.63
0.64
No
Annual Runoff
0.45
1.41
0.90
0.79
No
0.60
0.64
No
650/39
Nonmonsoon Runoff
2.20
4.51
3.71
3.81
Yes
0.82
0.63
Yes
Monsoon Runoff
0.13
4.13
3.51
3.62
Yes
0.89
0.63
Yes
Annual Runoff
0.52
4.05
3.56
3.67
Yes
0.89
0.63
Yes
652/34
Nonmonsoon Runoff
0.98
1.30
1.69
1.56
No
0.75
0.64
No
Monsoon Runoff
0.14
1.24
1.75
1.93
No
0.76
0.64
No
Annual Runoff
0.14
1.57
1.57
1.72
No
0.75
0.64
No
660/27
Nonmonsoon Runoff
1.26
1.99
1.67
1.47
No
0.72
0.65
No
Monsoon Runoff
0.79
0.93
1.19
1.34
No
0.64
0.65
No
Annual Runoff
0.79
0.96
1.31
1.52
No
0.64
0.65
No
668.5/19
Nonmonsoon Runoff
0.38
2.56
2.67
2.49
Yes
0.89
0.66
Yes
Monsoon Runoff
0.19
1.20
0.93
1.12
No
0.80
0.65
No
Annual Runoff
0.19
1.66
1.14
1.35
No
0.81
0.65
No
670/39
Nonmonsoon Runoff
1.04
2.25
2.66
2.79
Yes
0.74
0.64
No
Monsoon Runoff
0.26
0.44
0.72
0.82
No
0.68
0.63
No
Annual Runoff
0.26
0.74
0.88
0.97
No
0.68
0.63
No
680/20
Nonmonsoon Runoff
1.11
0.82
0.76
1.27
No
0.65
0.65
No
Monsoon Runoff
0.56
0.77
1.01
1.08
No
0.71
0.65
No
Annual Runoff
0.56
0.74
0.92
0.94
No
0.69
0.65
No
681/15
Nonmonsoon Runoff
0.44
1.99
2.34
0.07
No
0.66
0.66
No
Monsoon Runoff
0.87
0.41
0.22
0.18
No
0.72
0.66
No
Annual Runoff
0.87
0.12
0.31
0.06
No
0.68
0.66
No
684/10
Nonmonsoon Runoff
0.55
0.72
0.96
0.14
No
0.74
0.67
No
Monsoon Runoff
0.55
1.61
1.70
1.63
No
0.85
0.68
No
Annual Runoff
0.55
1.61
1.71
1.55
No
0.86
0.68
No
690/39
Nonmonsoon Runoff
1.82
2.71
3.01
3.21
Yes
0.77
0.64
Yes
Monsoon Runoff
0.26
3.80
4.63
4.82
Yes
0.82
0.63
Yes
Annual Runoff
2.20
4.11
4.64
4.85
Yes
0.82
0.63
Yes
695/26
Nonmonsoon Runoff
1.45
1.94
1.88
1.99
No
0.82
0.65
Yes
Monsoon Runoff
0.00
1.53
1.37
1.43
No
0.77
0.65
No
Annual Runoff
0.96
1.25
1.17
1.19
No
0.73
0.65
No
Table 4. Summary of test statistics and trend status
Station No./Data Length (Yr)
Description
Mann Kendall test
Spearman's Rho test
TheilSen's Slope
Remarks for trend
600.1/19
Nonmonsoon Runoff
3.01
2.79
192.83
Negative Trend
Monsoon Runoff
2.94
2.75
162.09
Negative Trend
Annual Runoff
3.01
2.79
192.83
Negative Trend
602/24
Nonmonsoon Runoff
1.02
0.79
5.23
No Trend
Monsoon Runoff
0.77
0.62
2.78
No Trend
Annual Runoff
1.02
0.79
5.23
No Trend
602.5/22
Nonmonsoon Runoff
2.26
2.28
0.90
Positive Trend
Monsoon Runoff
1.75
1.88
2.48
No Trend
Annual Runoff
0.56
0.73
0.86
No Trend
604.5/30
Nonmonsoon Runoff
1.53
1.45
15.85
No Trend
Monsoon Runoff
1.75
1.90
59.88
No Trend
Annual Runoff
1.36
1.60
46.48
No Trend
606/20
Nonmonsoon Runoff
1.59
1.39
44.11
No Trend
Monsoon Runoff
2.95
3.06
277.47
Negative Trend
Annual Runoff
2.76
2.78
239.66
Negative Trend
610/33
Nonmonsoon Runoff
3.33
3.21
4.62
Positive Trend
Monsoon Runoff
0.70
0.44
4.03
No Trend
Annual Runoff
1.44
1.08
8.89
No Trend
620/42
Nonmonsoon Runoff
4.10
3.84
2.15
Positive Trend
Monsoon Runoff
2.30
2.41
6.44
Positive Trend
Annual Runoff
2.71
2.74
8.95
Positive Trend
627.5/15
Nonmonsoon Runoff
0.99
1.43
1.25
No Trend
Monsoon Runoff
0.20
0.36
2.61
No Trend
Annual Runoff
0.40
0.49
4.39
No Trend
630/37
Nonmonsoon Runoff
0.98
1.07
2.99
No Trend
Monsoon Runoff
3.96
3.87
58.59
Negative Trend
Annual Runoff
3.73
3.75
60.29
Negative Trend
640/22
Nonmonsoon Runoff
1.52
1.65
0.28
No Trend
Monsoon Runoff
0.28
0.57
0.26
No Trend
Annual Runoff
0.06
0.13
0.08
No Trend
647/29
Nonmonsoon Runoff
2.01
1.90
3.65
Different Result
Monsoon Runoff
0.66
0.54
5.19
No Trend
Annual Runoff
0.62
0.62
6.44
No Trend
650/39
Nonmonsoon Runoff
0.75
0.82
0.34
No Trend
Monsoon Runoff
0.48
0.94
0.70
No Trend
Annual Runoff
0.19
0.85
0.65
No Trend
652/34
Nonmonsoon Runoff
0.50
0.43
3.02
No Trend
Monsoon Runoff
1.22
1.30
43.68
No Trend
Annual Runoff
0.86
1.15
46.30
No Trend
660/27
Nonmonsoon Runoff
0.38
0.25
0.66
No Trend
Monsoon Runoff
0.17
0.24
1.22
No Trend
Annual Runoff
0.04
0.04
1.24
No Trend
668.5/19
Nonmonsoon Runoff
3.05
2.98
2.07
Positive Trend
Monsoon Runoff
1.02
1.24
6.54
No Trend
Annual Runoff
1.23
1.44
8.07
No Trend
670/39
Nonmonsoon Runoff
0.70
0.54
1.75
No Trend
Monsoon Runoff
0.22
0.39
2.87
No Trend
Annual Runoff
0.05
0.38
1.47
No Trend
680/20
Nonmonsoon Runoff
1.24
0.62
20.20
No Trend
Monsoon Runoff
1.78
1.82
269.77
No Trend
Annual Runoff
1.72
1.80
275.84
No Trend
681/15
Nonmonsoon Runoff
2.08
1.95
46.47
Positive Trend
Monsoon Runoff
0.79
0.64
222.39
No Trend
Annual Runoff
1.09
1.12
326.41
No Trend
684/10
Nonmonsoon Runoff
1.61
1.69
24.51
No Trend
Monsoon Runoff
2.15
2.09
303.42
Negative Trend
Annual Runoff
2.15
2.09
342.94
Negative Trend
690/39
Nonmonsoon Runoff
0.48
0.68
3.58
No Trend
Monsoon Runoff
1.89
2.32
61.84
Different Result
Annual Runoff
1.72
2.28
59.86
Different Result
695/26
Nonmonsoon Runoff
1.37
1.65
41.89
No Trend
Monsoon Runoff
0.79
0.60
137.09
No Trend
Annual Runoff
0.40
0.37
65.85
No Trend


CONCLUSION
Nonstationarity on the annual peak discharge and average annual and seasonal runoffs on 21 stations of Koshi basin has been analysed. Many stations show the dependence and trend. So the nonstationarity behaviour in hydrological data series cannot be disregarded. Thus the nonstationarity shall be considered in the prevailing practice of flood frequency analysis to minimize the risk associated due to nonstationary characteristics of the hydrological time series.
REFERENCES

Ceschia, M., Linussio, A. and Micheletti, S. (1984). Trend Analysis of Mean Monthly Maximum and Minimum Surface Temperature of the 19511990 period in FriuliVenezia Giulia. Il Nuovo Cimento C, 17(4), 511521.

DHM (2006). Hydrological Records of NepalStreamflow Summary. Department of Hydrology and Meteorology, Ministry of Environment Science and technology, Government of Nepal, Kathmandu.

Effron, B. (1979). Bootstrap methods: another look at jackknife.
Ann.Statist.,7:126

Goel, N.K. (2013). Stochastic Hydrology. Lecture notes. Department of Hydrology, IIT Roorkee.

Hirsh, R.B. (2010). A Perspective on Nonstationarity and Water Management. Colorado Water Institute, Information series No. 109.

Hurst, H.E. (1951). Long term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng., 116:770543.

Jigajinni, R.B. (2001). Estimation of Flood Quantiles from Non stationary Flood Series. Thesis Report.Department of Hydrology, IIT Roorkee.

Kendall, M. G. (1973). Time series. Griffin. ISBN 0852642202

Kendall, M.G. (1975). Rank Correlation methods. Griffin, London.

Kendall and Stuart (1976). The Advanced Theory of Statistics. Vol.3. Charles Griffin, London.

Lye, L. M., and Lin, Y. (1994). Longterm dependence in annual peak flows of Canadian rivers. Journal of Hydrology 160, 89103.

Mann, H.B. (1945). Nonparametric tests against trend. Econometrica.13.245259.

Madansky, A. (1988). Prescriptions for working statisticians. Springer, New York.

Milly, P.C.D. et al. (2008). Stationarity Is Dead: Whither Water Management?. Ground Water News & Views, 4(1), 68.

Mondal, A., Sananda, K., and Mukhopadhyay, A. (2012). Rainfall Trend Analysis by MannKendall Test: A Case Study Of NorthEastern Part Of Cuttack District, Orissa. International Journal of Geology, Earth and Environmental Sciences,2(1), 7078.

Nayava, J.L. (1980). Rainfall in Nepal. The Himalayan Review, 12, 118.

Salas, J. D. and Obeysekera, J. (2014). Revisiting concepts of Return Period and Risk for Nonstationary Hydrologic Extreme Events. Journal of Hydrologic Engineering, 19(3), 54568.

Sen, P.K. (1968). Estimates of the regression coefficient based on Kendalls tau. J.Am.Stat.Assoc.63, 13791389

Sharma, C. K. (1979). Partial drought conditions in Nepal. Hydrological Sciences Journal, 24(3), 327333.

Sneyers,R. (1990). On the statistical analysis of series of observations. World Meteorological Organization, Technical Note No.143. WMO No.145.

Theil H. (1950). A rank invariant method of linear and polynomial regression analysis. I,II,III.Nederl.Akad.Wetensch.Proc.53,386392.

World Meteorological Organization (2012). A Note on Stationarity and Nonstationarity.

Yevjevich, V. (1972). Stochastic Processes in Hydrology. Water Resource Publication, Fort Collins, CO, USA.