• Box–Cox transformation;
  • Monte Carlo simulation;
  • seasonal variation;
  • tipping bucket rain gauges;
  • waiting times

A time series of tipping bucket recordings of very high temporal and volumetric resolution precipitation is modelled using Markov chain models. Both first and second-order Markov models as well as seasonal and diurnal models are investigated and evaluated using likelihood based techniques. The first-order Markov model seems to capture most of the properties of precipitation, but inclusion of seasonal and diurnal variation improves the model. Including a second-order Markov Chain component does improve the descriptive capabilities of the model, but is very expensive in its parameter use. Continuous modelling of the Markov process proved attractive because of a marked decrease in the number of parameters. Inclusion of seasonality into the continuous Markov chain model proved difficult. Monte Carlo simulations with the models show that it is very difficult for all the model formulations to reproduce the time series on event level. Extreme events with short (10 min), medium (60 min) and long (12 h) durations were investigated because of their importance in urban hydrology. Both the descriptive likelihood based statistics and the predictive Monte Carlo simulation based statistics are valuable and necessary tools when evaluating model fit and performance. Copyright © 2012 John Wiley & Sons, Ltd.