Modelling under uncertainty: Monte Carlo methods for temporally varying parameters

Uncertainty enters the modelling world through a variety of routes. Parameter values are not always known with adequate precision, and they may vary in time and/or space due to processes, which are not included in the model. One of the more popular methods by which the effect of uncertainty is incorporated into numerical models is the use of randomised methods based on Monte Carlo techniques in which parameters are randomly sampled from underlying probability distributions. However, in the case of temporally varying parameters, some care is required in the use of Monte Carlo methods and in the interpretation of model results. This short note addresses the problem of applying Monte Carlo techniques in the case of temporally varying parameters. It is shown that the correct approach is to resample the parameters at a time interval equal to double the decorrelation time of the parameter. This is illustrated with reference to a simple model of algal growth.