Ombrian curves: from theoretical consistency to engineering practice

One of the major tools in hydrological design is the ombrian curves, more widely known by the misnomer rainfall intensity-duration-frequency (IDF) curves. An ombrian curve is a mathematical relationship estimating the average rainfall intensity over a given timescale for a given return period. Several forms of ombrian curves are found in the literature, most of which have been empirically derived and validated by the long use in hydrological practice. Attempts to give them a theoretical basis have often used inappropriate assumptions (e.g. simple scaling) and resulted in oversimplified relationships that are not good for engineering studies. In a previous study, we have derived theoretically consistent ombrian curves based on a probability distribution suitable for describing the average rainfall intensity over a wide range of timescales (from sub-hourly to yearly). The mathematical form of those theoretically derived ombrian curves is not as simple as other widely used forms in practice. In this study, we present simplified ombrian relationships, which are approximations of the theoretically consistent one for a typical range of timescales, suitable for use in hydrological engineering.