Simulation - 7 - Weather and Rain Forecasts

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Simulation

Case/Problem:
The occurrence of rain in a region on a day is dependent upon whether it rained on the previous day.
(I) Rain on previous day:
Event: No rain 1 cm 2 cm 3 cm 4 cm 5 cm
Prob: 0.50 0.25 0.15 0.05 0.03 0.02

(II) No rain on previous day
Event: No rain 1 cm 2 cm 3 cm
Prob: 0.75 0.15 0.06 0.04
Simulate the region's weather for 10 days and determine by simulation the total number of days without rain as well as the total rainfall during that period. Use the following random numbers for simulation: 67, 63, 39, 55, 29, 78, 06, 78, 76
Assume that for the first day of the simulation it had not rained the day before.

Monte Carlo Method:
The ‘Monte Carlo’ simulation technique involves conducting repetitive experiments on the model of the system under study, with some known probability distribution to draw random samples (observations) using random numbers. If a system cannot be described by a standard probability distribution such as normal, Poisson, exponential, etc, an empirical probability distribution can be constructed. The Monte Carlo simulation technique consists of the following steps:
(1) Setting up a probability distribution for variables to be analyzed.
(2) Building a cumulative probability distribution for each random variable.
(3) Generating random numbers and then assigning an appropriate set of random numbers to represent value or range (interval) of values for each random variable.
(4) Conducting the simulation experiment using random sampling.
(5) Repeating Step – 4 until the required number of simulation runs has been generated.
(6) Designing and implementing a course of action and maintaining control.

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