Earth Science 340a - Physical Hydrology
September 27, 28 2001
Assignment 3: Precipitation - Probability & Statistics
Exceedence Probabilities and Return Periods
1)Table 2.1 in your text (Hornberger) gives average annual precipitation data for four cities Data for Denver and Washington can be found in the spreadsheet Eslab\Earthnt\Public\ES340a\Dataset_lab3.xls.
a)Calculate the mean and standard deviation for each set of precipitation values.
b)Plot the data for these two cities on a Frequency vs. Annual Precipitation histogram, (similar to Figure 2.6 in text) using the frequency function in Quattro Pro or Excel.
c)Briefly discuss whether the data conforms to a normal distribution.
d)Briefly discuss what problems you might see from any of the frequency distributions.
2)Using the method outlined in example 4.4 (pgs. 69-71 class lecture notes) compute the exceedence probabilities for each data set. Plot the data on arithmetic probability paper and interpolate by fitting a smooth curve or line to the data.
a)Compute the 10, 25, and 50 year return period rainfalls.
b)Compute the 100 year return period rainfall and comment on your confidence in its value
c)What chance (as % exceedence probability) is there that average annual precipitation will exceed 500 mm in Denver and 1000 mm in Washington?
3)Using the “z-value” method (pgs. 26-28 Hornberger) re-calculate the chance and return period of rains exceeding 500 mm (average annual) in Denver and 1000 mm (average annual) in Washington.
4)Using the “z-value” method calculate the chance and return period of an average annual rainfall exceeding 1500 mm in Washington. Comment on your confidence in this value, based on your plot in question (1).
5)Compare your probability (chance) and return period calculated in question (4) with the probability and return period calculated using your plot constructed in question (2) for a 1500 mm average annual rainfall in Washington.