Abstract: The accuracy of hydrological design values directly affects the engineering scale to be determined. A polynomial normal transformation (PNT) method is used in this study to estimate the design values (in quantile) of annual runoff at given frequencies to improve the accuracy of hydrological frequency calculations. We use a Monte Carlo method in numerical simulations and compare four calculation methods of third-order polynomial coefficients: product-moment (PM) method, L-moments (LM), least-square (LS) method, and Fisher-Cornish (FC) asymptotic expansion method . And a third-order polynomial normal transformation method is used to calculate the frequencies of the natural annual runoff at five stations in the Yellow River Basin. The results show that the polynomial coefficients obtained using the four methods give good estimates of the annual runoff design values at given frequencies, and the design value sequences fit well with the measured sequences. In the accuracy of normality conversion and data fitting, a list from high to low is LS method, LM method, FC method and PM method.

Key words: polynomial normal transformation method, flood frequency, Monte-Carlo method, Yellow River basin, fitting effect