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The main points i the stochastic hydrology are listed below:Probability Plotting, Graphical Construction, Normal Distribution Table, Arithmetic Scale Plot, Transformation Plot, Plotting Position, Empirical Methods, California Method, Formulae for Exceedence Probability
Typology: Study notes
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Graphical construction:
4 z 0 2 4 6 8 0 0 0.008 0.016 0.0239 0. 0.1 0.0398 0.0478 0.0557 0.0636 0. 0.2 0.0793 0.0871 0.0948 0.1026 0. 0.3 0.1179 0.1255 0.1331 0.1406 0. 0.4 0.1554 0.1628 0.17 0.1772 0. 0.5 0.1915 0.1985 0.2054 0.2123 0. 0.6 0.2257 0.2324 0.2389 0.2454 0. 0.7 0.258 0.2642 0.2704 0.2764 0. 0.8 0.2881 0.2939 0.2995 0.3051 0. 0.9 0.3159 0.3212 0.3264 0.3315 0. 1 0.3413 0.3461 0.3508 0.3554 0.
z (Partial tables shown here)
Arithmetic scale plot: 6
-‐ -‐ -‐ 0 1 2 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Z F(Z)
0.01 0.05 0.1 0.2 (^) 0.4 0.5 0.6 0.7 0.8 0.9 (^) 0.95 0. Transformation plot: 7
F(Z) (probability scale) F(Z) (arithmetic scale)
Formulae for exceedence probability: California Method: Limitations
( (^) m )
Hazen s formula: Chegodayev s formula: 15
( )
m
( )
m
Weibull s formula:
( )
m
Ref: Cunnane, C., Unbiased plotting positions – a review, J,Hydrol., Vol. 37, pp.205-222, 1978
Ref: Gumbel, E. J., 1958. Statistics of Extreme Values, Columbia University Press, New York
The Weibull plotting position formula meets all the 5 of the above criteria. 1.All the observations can be plotted since the plotting positions range from 1/(n+1) (which is greater than 0) to n/(n+1) (which is less than 1). 2.The relationship lies between (m – 1)/n and m/n for all values of m and n. 22
( )
m
Ref: Statistical methods in Hydrology by C.T.Haan, Iowa state university press