HYDROLOGY Lecture 12 Probability Assoc.Prof. dr.tarkan erdik
What it is – Descriptive statistics Unit Hydrograph Descriptive statistics include the numbers, tables, charts, and graphs used to describe, organize, summarize, and present raw data. central tendency (location) of data. i.e. where data tend to fall as measured by the mean, median, and mode. dispersion (variability) of data. i.e. how spread out data are as measured by the variance and its square root, the standard deviation. skew (symmetry) of data i.e. how concentrated data are at the low or high end of the scale as measured by the skew index. kurtosis (peakedness) of data. i.e. how concentrated data are around a single value as measured by the kurtosis index.
Coefficient of variation: Coefficient of variation is a nondimensional parameter defined as the standart deviation to its mean
FREQUENCY ANALYSIS- Frequency Analysis of Continuous Variables
Dicle during 1956-75 are given below: Example: Please calculate probability values of The flood data (m3/s) of the river Dicle during 1956-75 are given below: i Unit Hydrograph Year 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 X 2324 6300 2340 2080 2262 1250 3014 7910 4350 2630 Year 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 X 8820 4516 4866 6450 2250 3450 5300 963 2571 The probability of being equal to or remaining smaller than xm is calculated by the Weibull formula, Eq.3.7. .
m 1 2 3 4 5 6 7 8 9 10 xm 963 1250 2080 2250 2262 2340 2424 2571 2630 3014 F(xm) 0.048 0.095 0.143 0.190 0.238 0.286 0.333 0.381 0.429 0.475 i Unit Hydrograph m 11 12 13 14 15 16 17 18 19 20 xm 3450 4350 4516 4866 5300 5772 6300 6450 7910 8820 F(xm) 0.524 0.571 0.619 0.667 0.714 0.762 0.810 0.857 0.905 0.952 The probability that the flood discharge exceeds 8820 m3/s can be read from the table as 1-F(8820)=1-0.95=0.05 .
Dataset (original) Year Peak discharge (m3/s) 1996 2500 1997 4500 1998 3000 1999 2980 2000 2100 2001 1250 2002 3014 2003 8500 2004 4350 2005 6200 2006 7500 2007 4550 2008 4866 2009 6450 2010 6052 2011 2012 3580 2013 5335 2014 650 2015 2978 i Please calculate the probability that the flood discharge exceeds 6052 m3/s Unit Hydrograph
i Unit Hydrograph 0.76 6052 m3/s
i Unit Hydrograph
i Unit Hydrograph