What Large Sample Size Is Sufficient for Hydrologic Frequency Analysis?—A Rational Argument for a 30-Year Hydrologic Sample Size in Water Resources Management

Abstract

The calculation of hydrologic frequency is an important basic step in the planning and design stage of any water conservancy project. The purpose of the frequency analysis is to deduce the hydrologic variables under different guarantee rates, and to provide hydrologic information for water conservancy project planning and design. The calculation of hydrologic frequency requires that the sample size is large enough, as only then can the statistical characteristics of samples take the place of the total statistical eigenvalues. This means that the samples can reveal the statistical characteristics of hydrologic variables and identify the randomness rule of hydrologic phenomena. Many countries in the East Asian monsoon climate zone (China, Japan and South Korea) have stipulated a sample size of 30 years for hydrologic frequency analysis. In this paper the rationality of the 30-year sample size is proved by analyzing the periodic and random rules of hydrologic phenomenon and the influencing mechanism of solar activity, and by adopting the general conclusion of the sampling theorem. Then, using the wavelet analysis method to examine annual precipitation data in a long series generated from representative precipitation observation stations in China, the strong-weak cycle of solar activity is proved to be 10 years, which is consistent with the wet-dry cycle of the representative precipitation stations (10–12 years). Finally, adopting numerical modeling to analyze the normal distribution of randomly generated samples and long-range annual precipitation data collected from representative stations, hypothesis testing (u, F and t) is used to prove that a 30-year sample size is reasonable. This research provides a reference as to how to prove the necessary sample size for relevant statistical analyses (for example, how large the sample should be for analyzing hydrologic factors trend evolution, hydrologic data consistency and ergodicity of statistical samples), thus ensuring the reliability of the analytical results.

Keywords

• hydrologic frequency calculation
• sample size
• sampling theorem
• solar activity period
• hypothesis verification