## 1 Introduction  
IPCC's Assessment Report 6 (AR6) noted that human activities have contributed to an increase of 1.09 \({}^{\circ}\)C in global temperature since industrialization [1]. A global concern has been raised due to the climate change issues caused by temperature rise. In addition to affecting rainfall, runoff, infiltration, evaporation, and other components of the water cycle [2], climate change will also change the distribution of regional water resources [3] and increase the frequency and scale of rainstorms and floods [4, 5]. Lots of researches have demonstrated that there have been more global floods than ever before since 2000 [6], which has aggravated farmland waterlogging and adversely affected human production activities and food security [7]. One of the most common agricultural disasters is farmland waterlogging caused by excessive rain. On the one hand, farmland waterlogging affects crop growth, lowers the activity of the soil's microbial population [8], and influences the productivity of the land [9, 10]. It is reported that farmland waterlogging decreases crop yield by 32.9% on average [11]. On the other hand, farmland waterlogging causes pesticides and fertilizers to enter the water cycle, which increases the risk of water pollution and salinization [12], causes agricultural non-point source pollution, and damages the agricultural environment [13]. Sustainable crop production depends on effective farmland drainage, which is also a key solution to farmland waterlogging. A reasonable scale of drainage system can ensure crop growth and food security. Therefore, it is very important to determine the design parameters of the surface drainage system. Usually, a surface drainage system is designed based on the removal rate of excess surface water, which is expressed as the water depth drained off from a given area in a day or the design discharge per unit area, termed as the surface drainage coefficient [14]. The drainage coefficient is the main index for determining the scale and capacity of the surface drainage system. The drainage coefficient for any region varies with the geographical locations; land use; size of the area; rainfall intensity, frequency, and duration; and other climatic factors. The key to determine the drainage coefficient is the estimation of surface runoff. At present, the commonly used surface runoff calculation methods include the runoff coefficient method, the infiltration curve method, the excess water storage method, the SCS-CN, etc. Internationally, the runoff coefficient method was proposed in the 1930s [15], and was often used to calculate the runoff of urban impervious surfaces where evaporation and infiltration are negligible. China began to study runoff coefficient in the 1950s and has established a complete set of runoff coefficient values so far [16]. The principle of the infiltration curve model is that the rainwater after deducting evaporation, vegetation interception, infiltration, and groundwater storage in the basin is surface runoff. Infiltration calculation includes the Horton formula [17], Green-Ampt formula [18] and the Philip formula [19]. In the 1960s, China first proposed the excess water storage model, called the Xin'anjiang model [20], assuming the rainwater would be fully converted into runoff when the soil water content in the aeration zone reached the field water holding capacity. The Soil Conservation Service-Curve Number (SCS-CN) method, developed by the National Resources Conservation Service (NRSC), United States Department of Agriculture in 1969, was used for estimating direct runoff depth based on rainstorm depth [21]. This method was relatively easy to use, simple in structure, suitable for small catchment, and has been widely used in runoff estimation all over the world. Italy, Spain, Greece, and France are countries that widely use the continuation method and the movement method to calculate surface runoff [22; 23]. In a word, the water balance principle is the essence of all runoff calculation methods [24].