Problem

Using statistics for Siletz River peak flows, 1979-1999 (Table 1), generate a series of no...

Using statistics for Siletz River peak flows, 1979-1999 (Table 1), generate a series of normally distributed synthetic streamflows by following these guidelines.

(a) By performing a regression of flows for the period 1980-1999 vs. flows during 1979-1998, verify that the serial correlation coefficient for this time period is 0.1411.
(b) Verify that the mean and unbiased standard deviation for the full 21-year period are 19,343 cfs and 7217 cfs, respectively. Use these values for part (c).
(c) The list of 21 N(0,1) random numbers below was generated in Excel using the Tools/Data Analysis/Random Number Generation option with a seed of 12345. (The option for a seed allows one to generate identical sequences of random numbers.) Assuming that the initial flow = mean (at “step 0”), generate a sequence of 21 random flows using Equation. Compute the mean, standard deviation, and serial correlation coefficient of the synthetic flow sequence to see how well these statistics are preserved. Optional: Create a new series of N(0, 1) random numbers and repeat the generation. Notice that as the mean and standard deviation of the random numbers differ from 0 and 1, respectively, so do the mean and standard deviation of the synthetic sequence differ from their historic values.

Table

n 0	z n/a	n	z	n	z
i	−0.7341	8	−0.9733	15	−0.5506
2	0.2143	9	1 .21 1 9	16	−0.1774
3	0.7968	10	0.5659	17	0.4409
4	0.4544	11	−0.1092	18	−0.4908
5	−0.9235	12	−0.1214	19	0.8266
6	0.5659	13	0.3157	20	−1.1724
7	0.9885	14	0.4213	21	−0.4906

Table 1

Data and Frequency Analysis Computations for the Siletz River, at Siletz, Oreaon

Wate Year	Peak Flow (cfs)	Water Year	Peak Flow (cfs)	Water Year	Peak Flow (cfs)
1925	18,800	1950	16,400	1975	21,500
1926	16,800	1951	16,600	1976	23,600
1927	19,500	1952	19,400	1977	8630
1928	30,700	1953	24,600	1978	23,100
1929	11,200	1954	21,900	1979	16,600
1930	11,500	1955	21,200	1980	14,500
1931	34,100	1956	22,700	1981	26,500
1932	21,800	1957	20,900	1982	21,400
1933	19,800	1958	22,200	1983	18,300
1934	28,700	1959	14,200	1984	11,300
1935	15,000	1960	14,200	1985	13,600
1936	19,600	1961	24,400	1986	17,100
1937	16,100	1962	20,900	1987	20,000
1938	30,100	1963	26,300	1988	19,200
1939	17,800	1964	19,700	1989	15,400
1940	21,400	1965	32,200	1990	17,200
1941	13,200	1966	19,500	1991	20,500
1942	25,400	1967	19,100	1992	10,800
1943	26,500	1968	18,600	1993	12,000
1944	12,800	1969	14,500	1994	18,300
1945	22,400	1970	17,200	1995	18,800
1946	21,600	1971	18,100	1996	34,700
1947	28,000	1972	31,800	1997	22,700
1948	21,900	1973	19,700	1998	16,800
1949	29,000	1974	20,900	1999	40,500

Data were downloaded for USGS Gage Number 14305500 from the USGS website, http://water. usgs.gov/nwis/. The continuous record from 1925 has been used.

Equation