  We develop a numerical framework to implement the cumulative density function
(CDF) method for obtaining the probability distribution of the system state
described by a kinematic wave model. The approach relies on Monte Carlo
Simulations (MCS) of the fine-grained CDF equation of system state, as derived
by the CDF method. This fine-grained CDF equation is solved via the method of
characteristics. Each method of characteristics solution is far more
computationally efficient than the direct solution of the kinematic wave model,
and the MCS estimator of the CDF converges relatively quickly. We verify the
accuracy and robustness of our procedure via comparison with direct MCS of a
particular kinematic wave system, the Saint-Venant equation.
