Monte Carlo simulation is a popular method of risk and uncertainty analysis in oceanographic, atmospheric, and environmental applications. It is common practice to introduce a stochastic part to an already existing deterministic model and, after many simulations, to provide the user with statistics of the model outcome. The underlying deterministic model is often a discretization of a set of partial differential equations describing physical processes such as transport, turbulence, buoyancy effects, and continuity. Much effort is also put into deriving numerically efficient schemes for the time integration. The resulting model is often quite large and complex. In sharp contrast the stochastic extension used for Monte Carlo experiments is usually achieved by adding white noise. Unfortunately, the order of time integration in the stochastic model is reduced compared to the deterministic model because white noise is not a smooth process. Instead of completely replacing the old numerical scheme and implementing a higher-order scheme for stochastic differential equations, we suggest a different approach that is able to use existing numerical schemes. The method uses a smooth colored noise process as the driving force, resulting in a higher order of convergence. We show promising results from numerical experiments, including parametric uncertainty.