A joint probability approach to flood frequency estimation using Monte Carlo simulation

In the UK, flood estimation using event based rainfall–runoff modelling currently assigns pre-defined design values to the input variables which control the size of the flow events, apart from the rainfall magnitude which is treated as a random variable. The use of design values, rather than allowing the variables to be described by their full probability distribution, is a practical implification but may lead to biases in the output flood magnitudes. The present study simulates a large number of flow events using sets of input variables from distributions fitted to observed event data, taking into account seasonality. These simulated datasets are used for running a rainfall-runoff model, and a frequency analysis is applied to the peaks of the output flow hydrographs. The simulated inputs are the rainfall intensity and duration, and the soil moisture deficit (SMD) and initial river flow at the beginning of the rainfall event. An inter-event arrival time is simulated so that a series of events is obtained. The initial conditions of SMD and river flow of each event are made dependent on the (simulated) time elapsed since the previous event, and on the SMD at the end of the previous event.