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DRY PERIOD LENGTHS of ÇORUH RIVER BASIN Bihrat ONOZ Saffet OZTURK E. Beyhan YEGEN

DRY PERIOD LENGTHS of ÇORUH RIVER BASIN Bihrat ONOZ Saffet OZTURK E. Beyhan YEGEN Istanbul Technical University, Civil Engineering Faculty, Hydraulics Division, Istanbul, Turkey. In water resources development studies, determination of dry periods of flows plays an important role.

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DRY PERIOD LENGTHS of ÇORUH RIVER BASIN Bihrat ONOZ Saffet OZTURK E. Beyhan YEGEN

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  1. DRY PERIOD LENGTHS of ÇORUH RIVER BASINBihrat ONOZ Saffet OZTURK E. Beyhan YEGEN Istanbul Technical University, Civil Engineering Faculty, Hydraulics Division, Istanbul, Turkey

  2. In water resources development studies, determination of dry periods of flows plays an important role. • Droughts can be classified as agricultural, meteorological, hydrological, etc. and have significant effects on economical and social dimensions. • For the design of dams that will meet the water demand along dry periods and for estimation of economical and social effects of future droughts, analysis of statistical properties of dry periods is required. • For determination of dry periods of a flow series, run analysis (Yevjevich, 1967) method can be used. • With this analysis, lengths and return periods of dry periods can be determined.

  3. Run analysis are made with data for a single site or two and more sites, • a joint run length can be defined characterizing the dry period taking place during the same time period at the sites. • Time period during which X variable remains smaller than a given x0 value is defined as N- negative run length (or shortly run length); run length determines the drought duration at a given x0 level. • Research has shown that statistical properties of run length is only dependent on the serial dependence of the process. • In run analysis method, negative run length is defined as the period along which the flows remain continuously below a certain truncation level x0.

  4. DISTRIBUTION of NEGATIVE RUN LENGTH for SINGLE SITE PROCESSES for the case where observations are independent of each other the the expressions can be written: Here, p is the exceedance and q is the non-exceedance probabilities. . Downer et al (1967) have found the distribution of N-, negative run length, for infinite series case as follows:Here N- is an integer that can take any value between the range one to infinity.

  5. The probability mass function of negative run length has been given by Şen (1976) for dependent variable. • s, here, is a conditional probability and is expreesed in the following way: • The statistical magnitudes of negative run lengths of first order Markov processes are given below: • s conditional probability has been calculated by numerical integration for different values of q and p (Bayazıt and Şen, 1976).

  6. RETURN PERIOD of DRY PERIODS at A SINGLE SITE Bayazıt (2001) has obtained the followingexpressions for the drought return period at a site. for serially independent flows:

  7. Bayazıt (2001) has obtained the probability mass function of the joint run lengths at two separate sites analytically under the assumption that the flow series at the two sites are stationary. • DISTRIBUTION of JOINT NEGATIVE RUN LENGTH for TWO-SITE PROCESSES The expression of θ parameter of the geometric distribution is as follows: Conditional probability s is expressed as: The mean and variance of the run length can be found by the equalities given below:

  8. RETURN PERIOD of DRY PERIODS at TWO SITES • The return period of dry periods at two sites seen during the same years has been given by the following equation: • The probability that the flows of two sites remain smaller that the truncation level during the same years is:

  9. DISTRIBUTION of JOINT NEGATIVE RUN LENGTH for MULTISITE PROCESSES • Bayazıt and Onoz (2005) have obtained the distribution of joint run lengths of multivariate flows as follows: • The mean and variance of multivariate run lengths are given below: • θ parameter is determined as: Kendall and Stuart (1963) have given a simple expression for median truncation level (q = 0.5): • For more than three sites at the median level and for more than two sites at all the other trancation levels, the probability can be calculated using the computer programs (NIST, 2003) for the multivariate normal cumulative probabilities.

  10. RETURN PERIOD of DRY PERIODS at MULTISITE • T, the return period, can be calculated as the ratio of n, total length of the sample, to the expected number of runs. The following equation can be obtained for run length k,

  11. APPLICATION • In this work, the negative run lengths of flows and the return periods of the longest dry periods at stations 2304, 2305, 2315, 2316 and 2323 in Çoruh River Basin have been estimated by runs analysis and using the measured annual flow series at the stations. • This has been performed for 3 different cases. Firstly the case where the stations are individually independent but serially dependent has been analysed. Negative run lengths are determined for q = 0.5, 0.4 and 0.3 truncation levels. • Truncation levels have been determined under normal, lognormal distribution assumptions and empirically. Other than this, cases where 2, 3, 4 and 5 stations are serially and mutually dependent are investigated and the results are summerized below.

  12. CONCLUSIONS • In this study, the negative run lengths of flows and the return periods of the longest dry periods at stations 2304, 2305, 2315, 2316 and 2323 in Çoruh Basin have been estimated by runs analysis and using the measured annual flow series at the stations. • This has been performed for 3 different cases. Firstly the case where the stations are individually independent but serially dependent has been analysed. Negative run lengths are determined for q = 0.5, 0.4 and 0.3 truncation levels.Truncation levels have been determined under normal, lognormal distribution assumptions and empirically. • In the case where the flows were independent, the mean and the variance of the observations were close to the theoretical values. There are some variations for only station no. 2304 (q = 0.5 and 0.4) and station nos. 2305 and 2315 (q = 0.5). • the case where the flows were serially dependent, the mean and the variance of the observations were close to the theoretical values. Along with this, observation values were more close to the logarithmic theoretical values. • The maximum dry period length has been determined as 9 years at station no. 2304. The return period of the dry periods have been much greater in the independent case with respect to the case where they were dependent. The return period has been calculated as 1024 and 432 years for the independent and dependent cases respectively.

  13. the case where the 2 stations are serially and mutually dependent. The trucation level is only empirically determined. The joint negative run lengths have been found for q = 0.5. • The mean and variance values of the negative run legths of the observations were close to the theoretical values for 2304-2305, 2305-2315, 2305-2316, 2305-2323, 2315-2316, 2315-2323. • In the other cases differences have taken place. For 2304-2315, 2304-2323 and 2316-2323 cases the distribution of joint negative run lengths of observations and theoretical distribution were close to each other. • The maximum dry period length seen during the same years was 6 years for 2304-2305 case with a return period of 95 years.

  14. Finally the case where 3,4 and 5 stations are serially and mutually dependent. The joint negative run lengths have been found for q = 0.5. • The mean values of the negative run legths of the observations were close to the theoretical values for the 3 station case. • The maximum dry period length seen during the same years was 6 years for cases 2304-2305-2315, 2304-2305-2316, 2304-2315-2316, 2305-2315-2316 with a return period of 141, 94, 225 and 162 years respectively .

  15. In the case where 4 and 5 stations are serially and mutually dependent, the mean and variance of observations stay below the theoretical mean and variance. • The longest dry period for 4 stations is 3 years for 2305-2315-2316-2323 and 2304-2305-2315-2316 with a return period of 44 and 37 years. • 3-year dry period length seen at 3 stations changes between 21-25 years. • Return period of equal length dry period at 4 stations is longer with respect to 3 station case. The reason for this is that the probability of annual flows remaining smaller than the truncation level at 4 stations is smaller than that at 3 stations.

  16. In this work, by using the past observations of the Çoruh River Basin, dry periods and the return periods of the longest dry periods have been determined for the basin. • Çoruh River Basin, which is situated in Eastern Black Sea Region of Turkey, is one of regions receiving the maximum precipitation of the country. In this basin, at one, two and three stations long droughtnesses (9, 6 and 6 years) have been determined. At 4 stations a dry period of maximum 3 years and at 5 stations a dry period of maximum 2 years have been determined.

  17. Thank you

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