Investigations of Nonstationarity on Hydrological Data of Koshi Basin, Nepal

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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

  1. 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.

  2. METHODOLOGY

  1. Investigation Of Short Term Dependence

    1. 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

    2. 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)

      1. Annual flow series x

        x ,……..,x

        are assumed as

        5n 7

        1, 2 n

        independent observ s. Each x has the same

    3. Von Neumann Ratio Test (Madannsky, 1988)

      (x x )

      (x x )

      n

      2

      t t1

      ation i

      probability of occurrence, 1/n.

      1. 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.

      2. Hursts K is calculated for the bootstrap samples.

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

      4. 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

    4. Autocorrelation Test (Yevjevich, 1971)

      (5)

      counted.

      1. 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)

      1. 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.

        1. Mann-Kendall Test (Mann, 1945: Kendall, 1975)

  2. Investigation Of Long Term Dependence

  1. 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

  2. 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

  3. 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.

  1. 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.

    1. 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.

    2. 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

  2. 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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