Polynomial depth-duration-frequency curves

Abstract. Depth-duration-frequency (DDF) curves depict how much precipitation occurs on average in a given location during various time intervals once in a given return period. The standard approach to the construction of these curves assumes that the parameters governing the scaling behaviour of rainfall intensity with duration remain constant. We show that in regions where different meteorological processes control short- and long-duration extreme precipitation events, this approach is applicable only in limited time intervals. If the range is as wide as several minutes to several days, three parameters are not sufficient for representing the complexity of the DDF curve shapes. In fact, the curves are wave-shaped because convective and cyclonic precipitation occur for limited lengths of up to several hours and several days, respectively. Thus, we suggest applying polynomial functions of the sixth degree to generate smooth DDF curves that fit design precipitation totals for individual time intervals. Nevertheless, return values need to be fitted against logarithmic time intervals instead of only time. These polynomial DDF curves suitably represent extreme precipitation statistics even in orographically influenced locations where already the precipitation maxima of several hours can be caused by cyclonic precipitation events.