We develop a phenomenological model of suspended-sediment transport on the basis of data acquired in the Capesterre river, which drains a small tropical catchment in Guadeloupe. The model correctly represents the transport of suspended sediment during floods, provided that the relation between concentration and water-level forms a counterclockwise loop. In the model, the properties of the sediment and of the river are all lumped into four parameters: a settling velocity related to the size of the suspended sediment, a threshold water-level which acts as a proxy for the threshold shear stress, a characteristic erosion rate and a dimensionless exponent, both of which are related to the availability of fine sediment. The assimilation of field data to our model shows that the value of the parameters change from one flood to the next, probably reflecting changes in the characteristics of the river and the sediment. Finally, a test of the model against data acquired in a small catchment in the french Alps, suggests that the model is versatile enough to be used in diverse hydrological settings.