Regional flow–duration–frequency model for the tropical island of Martinique

The discharge data from seven hydrographic stations in Martinique, a tropical Caribbean island, were used to establish first a ‘discharge–duration–frequency’ model (QdF model) according to a new version, called the ‘continuous convergent model’. The validity of the hypotheses was verified: convergence of the Gumbel probability distribution functions for the mean discharges of different durations, similarity of these distributions according to hyperbolic function. For Martinique, the model was simplified by adopting a unique convergence point of the Gumbel lines for all the stations, corresponding to an inter-annual discharge equal to zero. In a second step, once the model had been established for the seven stations, a unique regional transcription was assessed. This involved the use of normalised hydrological data, with two characteristic indices of flood formation on a catchment: the 10-year peak discharge and a characteristic duration of the floods on each basin. From this normalisation it was possible to compare successfully the results of the QdF model obtained on each basin. The resulting normalised regional model is made up of two relationships giving the values of the two characteristic indices, and two statistical relationships giving the discharge quantiles, for all flood discharge durations and all return periods between 0.5 and 200 years. Finally, this model was compared to similar ones, which were obtained previously for temperate climate zones (in Europe).