**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):**24-04-2018 -
**ISSN (Online) :**2278-0181 -
**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 1951-1990 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 1951-90, in some stations of the Italian Hydrographic Service spread over the region of Friuli-Venezia 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 xi-1 < xi > xi+1 or xi-1 > 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 non-parametric bootstrap approach (Effron 1979) was used.

To test long-term 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 n-time 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 lag-one 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 long-term 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 Theil-Sens

r1 N n ,

n 2 n 2 1

(7)

slope estimator.

Mann-Kendall 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 Mann-Kendall 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

Theil-Sens 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 Meter-MCM) 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

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

No

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

Theil-Sen'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

Theil-Sen'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.

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