Investigations of Nonstationarity on Hydrological Data of Koshi Basin, Nepal

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

   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	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.

REFERENCES

1. Ceschia, M., Linussio, A. and Micheletti, S. (1984). Trend Analysis of Mean Monthly Maximum and Minimum Surface Temperature of the 1951-1990 period in Friuli-Venezia Giulia. Il Nuovo Cimento C, 17(4), 511-521.

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

3. Effron, B. (1979). Bootstrap methods: another look at jackknife.

   Ann.Statist.,7:1-26

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

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

6. Hurst, H.E. (1951). Long term storage capacity of reservoirs. Trans. Am. Soc. Civ. Eng., 116:770-543.

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

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

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

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

11. Lye, L. M., and Lin, Y. (1994). Long-term dependence in annual peak flows of Canadian rivers. Journal of Hydrology 160, 89-103.

12. Mann, H.B. (1945). Nonparametric tests against trend. Econometrica.13.245-259.

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

14. Milly, P.C.D. et al. (2008). Stationarity Is Dead: Whither Water Management?. Ground Water News & Views, 4(1), 6-8.

15. Mondal, A., Sananda, K., and Mukhopadhyay, A. (2012). Rainfall Trend Analysis by Mann-Kendall Test: A Case Study Of North-Eastern Part Of Cuttack District, Orissa. International Journal of Geology, Earth and Environmental Sciences,2(1), 70-78.

16. Nayava, J.L. (1980). Rainfall in Nepal. The Himalayan Review, 12, 1-18.

17. 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), 54-568.

18. Sen, P.K. (1968). Estimates of the regression coefficient based on Kendalls tau. J.Am.Stat.Assoc.63, 1379-1389

19. Sharma, C. K. (1979). Partial drought conditions in Nepal. Hydrological Sciences Journal, 24(3), 327-333.

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

21. Theil H. (1950). A rank invariant method of linear and polynomial regression analysis. I,II,III.Nederl.Akad.Wetensch.Proc.53,386-392.

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

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