This GoldSim model simulates random daily precipitation using a first-order, 2-state Markov chain. A Markov chain (aka Markov process) changes between states randomly over time and the probability of a state change depends on the previous state. With the first-order Markov chain model, the probability of rain on a given day is conditioned on the wet or dry status of the previous day.
A Status element is used to represent the wet/dry state of the system. GoldSim changes the state using a an equation dependent on 2 state change probability inputs and a random number generated by a Stochastic element, triggered each day of the simulation.
Combined with the Markov process is a stochastically driven precipitation rate sampled from a gamma probability distribution based on statistics of observed precipitation records.
Another model (link below) calculates the input parameters to run this model. Just load the time series data into that model and it will produce the PWW, PWD and Mean/SDev values. The functionality of this model is taken from the WGEN Weather Simulator.
Download the Model File: