  The Advanced Circulation (ADCIRC) and Simulating Nearshore Waves (SWAN)
coupled model is modified to include a stochastic term in the shallow water
equations that represents random external forces from debris carried by surge
and short-term local scale atmospheric fluctuations. We added $\alpha$-stable
noise, uncorrelated in space and time, in the forcing terms of the coupled
model. Inputs to the model are unstructured computational mesh derived from
topography and bathymetry, land cover classification, tidal potential
constituents and atmospheric forcing. The model simulated surge height of
around five meters rushing at four meters per second near Tacloban City
downtown. Underestimation of simulated surge height is expected with use of
bare earth model and absence of fluid sources on the governing equations, while
overestimation of simulated peak height also occurs due to presence of concrete
barriers that reduced surge height and inundation extent. The stochastic model
is sensitive to random external forces during low tide and relatively higher
fluid speed. Low tide happens when the fluid speed is maximum and water
elevation is lowest, while higher fluid speed is brought by external forces
like storm surge. However, the difference of stochastic solutions from the
deterministic solution averages to zero and there is no significant improvement
of the storm surge model in general when it comes to additive noise. This is an
expected result since the noise used has zero mean. As $\alpha$ goes to zero
larger jumps occur more frequently so $\sigma$ needs to be as small as
$10^{-8}$ for simulation stability.
