Length of Data Necessary to Identify Distributions in Flood Frequency Analysis

One of the important problems in developing regional flood frequency distributions is deciding the particular distribution to use. This problem becomes difficult to resolve when the available data are small. The objective of the present study is to determine the data length needed to arrive at an acceptable flood frequency distribution. Indiana annual flood data were analyzed in this study to determine appropriate flood frequency distributions. Synthetic data sets of several lengths were generated to simulate peak annual flood flow sequences of various lengths. These synthetic data sets were generated by using random number generation and Generalized Extreme Value, Generalized Pareto, and Generalized Logistic Distributions. The parameters used for the distributions were calculated from the peak annual flow record from the Muscatatuck River in southern Indiana. Synthetic data sets were plotted on an L-moment diagram to determine how well the data set corresponded to the distribution from which it was generated. The data sets were compared by using L-kurtosis versus L-skewness diagrams of Generalized Extreme Value, Generalized Pareto, Generalized Logistic, Lognormal, and Pearson Type III Distributions. For a record length of 20 years, the average record length of most flood gages in Indiana, it was nearly impossible to determine the distribution from which the data set had been generated. As expected, correspondence to the correct distribution increased as synthetic record length increased. It remained difficult to determine the correct distribution until the record length was increased to 100 years. Even then, there was still large scatter dispersed around all of the distributions. The main conclusion from the study is that it is important to use long data sequences in flood frequency studies because with shorter sequences it is not possible to identify the correct distribution to be used.