Incorporating historical flood events in type-based statistics

Abstract

Flood statistics form the basis of many hydrologic designs. However, short observation periods can lead to a high degree of uncertainty in the quantile estimates, especially for extreme floods. One way to expand the information used in the statistics and, in particular, to include other exceptional floods in the sample is to take historical floods into account. The use of these floods, which are usually reconstructed from chronicles or flood marks, has long been established for classic flood frequency analysis. However, the fact that historical floods can also have different origins and are therefore not statistically identically distributed has so far been ignored. To avoid this violation of the statistical assumptions, we show how historical floods, subdivided according to their genesis, can be taken into account in type-based flood statistics. For this purpose, the classical partial probability weighted moment (PPWM) method is extended for the type-based mixture model of partial duration series (TMPS). The result is compared to a Markov chain Monte Carlo method in order to compare the differences between the two methods. Type-based statistics can also be used to attribute the different influences of historical floods on the quantile estimate. An example shows that floods associated with long-lasting precipitation in particular are overestimated in short samples, while heavy rainfall floods are comparatively well represented. The results show that the consideration of historical events in type-based statistics not only allows a more balanced view of extreme floods, but also enables the influences of these to be attributed.