Incorporating Non-Systematic Information to Flood Frequency Analysis Using the Maximum Likelihood Estimation Method

Abstract

Non-systematic information at a gauge station is defined as the censored information for a period prior to the systematic record. Depending on the source, we can distinguish between historical information and paleofloods. Non-systematic information can be classified according to the statistical analysis based on the type of censoring which generates it. When there is a given censoring limit, it is called censored information type 1. The value of non-censored floods may or may not be known. We will call it “censored information” (CE) when the K floods that exceeded the threshold level of perception during the non-systematic period of M length are known. If their values are unknown, it will be called “binomial censored” (BC). If there is no censoring limit, the information is called censored information type 2. In this case the K largest floods during the non-systematic period are known, K being a deterministic variable. As the largest paleoflood tends to remove the evidence left by other paleofloods, K is usually equal to 1; this information is called “maximum flood” (MF).

The Maximum Likelihood estimation method was chosen not only because of its statistical properties, but especially because of its ability to incorporate any kind of information easily in the estimation process. This is done by assuming the independence between annual floods and the construction of the corresponding joint probability density function for each type of flood information.