  We investigate the influence of uncertain data on solutions to initial
boundary value problems. Uncertainty in the forcing function, initial
conditions and boundary conditions are considered and we quantify their
relative influence for short and long time calculations. It is shown that
dissipative boundary conditions leading to energy bounds play a crucial role.
For short time calculations, uncertainty in the initial data dominate. As time
grows, the influence of initial data vanish exponentially fast. For longer time
calculations, the uncertainty in the forcing function and boundary data
dominate, as they grow in time. Errors due to the forcing function grows faster
(linearly in time) than the ones due to the boundary data (grows as the square
root of time). Roughly speaking, the results indicate that for short time
calculations, the initial conditions are the most important, but for longer
time calculations, focus should be on modelling efforts and boundary
conditions. Our findings have impact on predictions where similar mathematical
and numerical techniques are used for both short and long times as for example
in regional weather and climate predictions.
