Frequency Curves for Annual Flood Series with Some Zero Events or Incomplete Data

Abstract

In fitting a theoretical frequency distribution to a set of data, a problem arises if the series contains a number of zero values, as may occur in annual flood peak data for small, arid-region streams. The problem is twofold: first, commonly used distributions do not fit such a set of data; second, if a logarithmic transformation of the data is being used, logarithms of zero flows are not usable in a computation. To overcome the difficulties, a theorem of conditional probability is used. The probability of occurrence of a nonzero peak is combined with the conditional probability of exceeding a given flood magnitude, given that a nonzero peak has occurred. The method has been found useful also for fitting flood series in which information of peak annual floods below a specific stage is lacking.

Log Pearson type 3 quantile estimators with regional skew information and low outlier adjustments

“…B17 does not recommend using CPA when more than 25% of the observations are censored. CPA was originally developed by Jennings and Benson [1969] to account for the removal of zero-flow events from a systematic record before fitting the LP3 distribution. For LP3 and lognormal data, Kroll [1996] compares the precision of low-flow quantile estimates obtained with CPA to maximum likelihood estimation (MLE), log-probability-plot regression (LPPR), and partial probability weighted moments (PPWM) estimators.…”

Stochastic index model for intermittent regimes: from preliminary analysis to regionalisation

“…The problem of the presence of zero data can be solved using the theorem of total probability, which is used to determine the probability of occurrence of a non-zero event, given that a zero event has already occurred (Jennings and Benson, 1969). The theorem is given by:…”

“…However, this solution can create problems with the assumption of continuity made in frequency analysis. Jennings and Benson (1969) highlighted the potential problems encountered when a continuous distribution is fitted with data including zero values.…”

“…Several studies have focused on various methods to work with zero data in frequency analysis (e.g. Jennings and Benson, 1969;Kilmartin and Peterson, 1972;Haan, 1977;Wang and Singh, 1995), while others have concentrated more on techniques for working with censored data (e.g. Kroll and Stedinger, 1996;Tate and Freeman, 2000).…”

“…-The third is based on the theorem of total probability (Jennings and Benson, 1969). Woo and Wu (1989) and Wang and Singh (1995) developed empirical three-parameter models for the frequency analysis of hydrologic data containing zero values starting from the theorem of total probability.…”