Question

You are required to undertake a preliminary drought risk assessment for a major water supply catchment. A drought year is defined whenever the annual runoff is below 30 mm. Undertake a preliminary drought risk assessment the observed annual runoff data found in the file Assignment_3_Data.xls.

Using this data, undertake the following:

a. Use normal and log-normal probability plots to determine a suitable probability model for the runoff data. [4 marks]

b. Perform the Kolmogorov-Smirnov goodness of fit test for the normal and log-normal probability models. To get full marks in this question, you are required to formally write the null hypothesis, perform the test and make a formal conclusion. [5 marks]

c. Using the most suitable probability model, determine the probability of a drought occurring in any year. [1 mark]

Answer 1

(a)

Probability Plot of Annual Runoff (mm) Normal-95% CI 99.9 126.8 120.9 89 4.880 AD 95 p-value 0.005 80 U 60 U 50 30 20 10 -400 200 800 200 400 600 Annual Runoff(mm)

(b)

Probability Plot of Annual Runoff (mm) Lognormal-95% CI 99.9 4.431 Scale 0.9484 1H11 89 AD 0.320 95 P-Value 0.527 80 ー70 U 60 U 50 30 20 10 100 10 1000 Annual Runoff(mm)

(c)

From the above plot (a), it is observed that normal distribution is not a suitable model for this data set. Moreover the p-value of the test is < 0.005.

From the above plot (b), it is observed that log-normal distribution is suitable model for this data set. Moreover the p-value of the test = 0.527 is >0.05.