## 1 Introduction
In a practical application, the impact of climate, topography, underlying surfaces, and human activities on runoff should be comprehensively considered and the most suitable method should be chosen to calculate surface runoff. Some researchers have established the relationship among the drainage coefficient, catchment area and surface runoff, such as the Cypress-Creak formula in the United States and the empirical formula in China and the former Soviet Union [25; 26; 27]. These formulas are suitable for the drainage design of river channels and ditches in plain areas with large watershed areas. The Rational Formula [28] was proposed on the base of the empirical relationship between the peak runoff rate and rainfall intensity, runoff coefficient, as well as catchment area, which is mainly suitable for small catchments in hilly areas. The average draining formula, which is a suitable method for the drainage design of small plain basins, is to drain off the design runoff in the drainage area within the designed drainage duration, and the drainage coefficient can be obtained. [PERSON] et al. [29] analyzed the daily rainfall data of 21 years and calculated the drainage coefficient by using the simplified hydrological method, SCS-CN method, Cypress-Creak formula, and Rational formula. The results not only obtained the drainage flow of the surface drainage system, but also proved that the Rational formula was suitable for the design of river channels and outfalls. [PERSON] et al. [26] computed the drainage coefficient in the Luoshan drainage area by using the average draining formula and the empirical formula. The results showed that the drainage coefficient calculated by the average draining formula was greater than that calculated by the empirical formula for 1 day rainfall duration and was less than that calculated by the empirical formula for 3 day rainfall duration under the same return period. [PERSON] et al. [27]calculated and compared the drainage coefficient of the Huaibei plain calculated by the empirical formula and the average draining formula and adjusted the peak value relation index (m) in the empirical formula. It was found that if the drainage duration in the average draining formula was set as 1 day and m in the empirical formula was set as one, the calculation results of the two formulas were close and the adjusted m range was taken as 0.84-0.87, meaning that it was more reasonable to calculate the drainage flow of the Huaibei Plain using the empirical formula. In addition, Indian scholars calculated the drainage coefficient by subtracting the basic infiltration rate from the consecutive days maximum rainfall. [PERSON] et al. calculated the drainage coefficients of North Lakhimpur (Assam) [30] and Doimukh (Arunachal Pradesh), India, [14] for different return periods in 2008 and 2016, respectively. The former was primarily made up of loam with an infiltration rate ranging from 1 to 5 mm/h, whereas the latter was primarily made up of sandy soil with a basic infiltration rate of 10 mm/h. The results showed that the drainage coefficient with a 25-year return period was the largest, while the drainage coefficient with a 5-year return period was very small, and certain drainage measures were required for both regions. At the same time, the author did not consider evapotranspiration, surface retention, and raindrop interception. The average draining formula or the empirical formula is often used in China, but both methods have some drawbacks. The parameters in the empirical formula were determined based on hydrological observation data in the 1970s; whether the parameters meet the requirements of the current conditions needs further study. The maximum drainage flow in the drainage area is the design basis of the empirical formula, which considers the influence of runoff, area, and shape of the waterlogging area on the drainage coefficients, but does not consider the influence of drainage duration.