## 2 Data and Methods  
### Study Area and Storm Events  
The scope of this work covers two basins in the semi-humid regions of northern China: the Fuping catchment with eight rain gauges, and the Zijingguan catchment with eleven rain gauges. Figure 1 shows the gauge locations, DEMs, and WRF nested domains of the two study catchments. The Fuping and Zijingguan catchments, which respectively belong to the south and the north branch of the Daqing river catchment, occupy drainage areas of 2210 and 1760 km\({}^{2}\), respectively. The average annual rainfall in the Daqing river catchment was approximately 600 mm. From late May to early September each year, the warm and humid airflow around the tropical low pressure moves towards northern China. The airflow encounters subtropical high pressure and the Taihang Mountain topography to stop its movement and gradually slow down. There is weak cold air activity in the study areas, and cold and warm air interact with local strong convective rainfall.  
For the classification of the storm events, the temporal and spatial homogeneousness of the rainfall occurring in the two basins was analyzed by calculating the storm events coefficient of variance (\(Cv\)), since the lower the \(Cv\) value, the more homogeneous the rainfall [28]. \(Cv\) can be written as follows:  
\[C_{v}=\sqrt{\frac{\sum_{i=1}^{N}\left(\frac{x_{i}}{\overline{x}}-1\right)^{2}}{ N}} \tag{1}\]  
where \(\overline{x}\) is the average of \(x_{i}\). When the calculation is for the spatial distribution, the spatial \(Cv\) value calculated by Equation (1) means the variability of the spatial rainfall distribution, \(x_{i}\) is the 24 h rainfall accumulation of the \(i\)th station, and \(N\) is the number of rain gauges, hence the spatial \(Cv\) reflects an average of the cumulative deviation of all time steps at each rain gauge; when the calculation is for the time distribution, the temporal \(Cv\) means the variability of the temporal rainfall distribution, \(x_{i}\) is the catchment average rainfall of the \(i\)th-hour, and \(N\) is the total number of hours for the storm duration. At this time, the temporal \(Cv\) value represents an average of the cumulative deviation of all rain gauges in each time step.  
Figure 1: Locations and digital elevation models (DEMs) of the two study catchments in northern China with the gauges and the settings of the Weather Research and Forecasting model (WRF) nested domains.  
Unlike the southern regions of China, it is difficult to find truly homogeneous rainfall in northern China. The spatial \(Cv\) and temporal \(Cv\) of precipitation events that occurred in the two basins from 1985 to 2015 were separately sorted according to frequency. For both spatial \(Cv\) and temporal \(Cv\), there was a critical value of 5% frequency, which was taken as a \(Cv\) threshold value to separate homogeneous and inhomogeneous storm events [29]. That is to say, the temporal or spatial homogeneousness was determined when the \(Cv\) values of storm events were less than the threshold \(Cv\) values, which were 0.4 in time and 1.0 in space, respectively.  
Six typical and representative events in the two basins from 2005 to 2015 were selected for simulation and the detail rainfall information on the events and the judgment of the rainfall type are shown in Table 1, wherein the rainfall distribution of Type 1 (including Event 1) was homogeneous in both space and time, Type 2 (including Event 2) was homogeneous in space but inhomogeneous in time, and Type 3 (including the other four events) was inhomogeneous in both space and time. It should be pointed out that the soil moisture levels in Event 4 and Event 6 were relatively dry before raining, and Event 5 had the shortest rainfall duration and the largest accumulative rainfall of six storm events. There is a 24 h statistical window, which can completely cover the precipitation process of the selected storm events.