# Low Stream Flow Frequency Analysis with Ordinary and Tobit Regression

*by*Shiping Liu, North Carolina State Univ, Raleigh, United States,

Jery R. Steinger, North Carolina State Univ, Raleigh, United States,

**Document Type:**Proceeding Paper

**Part of:**Water Resources Planning and Management and Urban Water Resources

**Abstract:**In order to estimate the low-flow quantiles at ungaged sites, it is necessary to estimate low-flow quantiles at gaged sites. Two linear regression methods, denoted NR and NE, are compared for estimating the mean, standard deviation and low-flow quantiles when some annual low-flow values are zero or indistinguishable from zero. Results of a Monte Carlo simulation show that the NE method is better than the NR method. Methods for estimating the parameters of low-flow logarithmic regression models are needed for the situations where some of low-flow quantiles (the dependent variable in the regression model) are zero. Two methods which have been used to estimate the parameters of low-flow regression model are examined in this paper. One, denoted OLSC, adds a positive constant to all the low-flow quantiles before estimating the logarithmic regression model's parameters. The other, denoted OLSD, ignores all observations having zero low-flow quantiles then estimating the parameters of the regression model using ordinary least squares (OLS). The maximum likelihood estimation method for Weighted Tobit (WT) and Ordinary Tobit (OT) models are also used for estimating the parameters of the regional regression model since these methods include all observations without distortion. A Monte Carlo study shows that OLSC and OLSD on average provide poor parameter estimates. The WT and OT methods provide efficient parameter estimates of low-flow regression model based on the sampling mean square error (MSE).

**Subject Headings:**Regression analysis | Streamflow | Low flow | Parameters (statistics) | Frequency analysis | Errors (statistics) | Mathematical models | Monte Carlo method | Linear functions | Nebraska | North America | Europe | Monaco | United States | Monte Carlo

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