1. Introduction
Rainfall-runoff simulation is the basis of hydrological and soil erosion models. Scholars usually calculate runoff using infiltration models, such as Philip, Green-Ampt and Horton, but these model’s parameters are difficult to obtain [
1], and they have several parameters, which easily leads to the problem of overparameterization [
2]. The U.S. Department of Agriculture created the Soil Conservation Service curve number (SCS-CN) (nowadays Natural Resource Conservation Service Curve Number (NRCS-CN)) model based on rainfall events in the 1950s. The model only contains two parameters: the initial abstraction ratio (
λ) and the curve number (
CN). The
CN comprehensively reflects the influences of environmental factors on the runoff, such as soil type, soil moisture, land use and vegetation cover [
3]. Because the model is simple in structure, and can effectively predict the runoff, it has been applied to areas where there are no rainfall-runoff data. It has been promoted in many countries and regions, such as the United States, India, China, and the Mediterranean [
4,
5,
6,
7,
8].
In order to apply the model accurately and reasonably, the studies of the determination of its parameters under the influence factors (different region, land use), comparison to other models and improving the model structure have been carried out. How to determine the model’s parameters reasonably is especially important for the application of the model, for
CN is a sensitive parameter and has a great influence on the runoff volume prediction. Fu et al. [
6] studied the value of
CN in Beijing, while Li et al. [
9] studied the main influencing factors of potential maximum storage (
S) in the loess area of China. Zhou et al. [
8] studied the initial abstraction ratio in the loess area of China. Scholars also have done a lot of research on the differences between SCS-CN and other models. Rawls [
10] compared the difference between this model and Green-Ampt model and found that the accuracy of Green-Ampt was higher. Fu et al. [
1] compared the different runoff calculation methods in the Beijing area and drew the same conclusion. In order to improve the accuracy of this model, some changes and new parameters were put forward or combined into the model. Huang [
11] derived the relationship between slope and
CN value, while Chen et al. [
5] applied this relationship in hillslope cropland of purple soil. Jiao et al. and Rajib et al. [
12,
13] combined the soil evapotranspiration and moisture model into the original runoff model, and the prediction accuracy was improved. Mishra and Singh [
14,
15,
16] proposed an improved Mishra–Singh (MS) model by adding the pre-humidity to the model, Sahu improved MS to the Sahu–Mishra–Eldho (SME) model, and then added rainfall duration, and put forward the modified Sahu–Mishra–Eldho (MSME) model. All the above studies promoted the understanding and application of the model. However, the influence of rainfall intensities and duration on the parameters of the model has not been considered comprehensively in the existing studies.
In the beginning, rainfall was used as the basis of calculation, and the influence of rainfall intensities and duration was not taken into account [
17]. The parameters of the model provided in the National Engineering Manual, Hydrology Section 630 (NEH-630) is the median logarithmic frequencies derived from the annual maximum rainfall runoff. For all return periods, the
CN is taken to be same. Previous studies have shown that rainfall intensities and duration have an important impact on runoff production processes such as vegetation interception [
18], infiltration process [
19], etc., and will inevitably have an impact on the corresponding parameters in the model, such as initial abstraction (
Ia), infiltration (
F), etc., and then may affect the parameters of the model. Rawls [
10] and Fu et al. [
1] found that the Green-Ampt model had higher accuracy and the main reason was the SCS model did not take into account the influence of rainfall process on runoff generation. Sahu [
15] proposed the MSME model which combines the rainfall duration into the SCS, and the prediction efficiency of the model was improved. Although the study improved the accuracy, more parameters were added and the hypothesis that the runoff production factors follow the same hypothesis as the whole rainfall in the rainfall process had not been strictly proved, and the influence of rain intensities was not taken into account in the hypothesis.
Rainfall intensities and duration are important hydrological factors which are inversely correlated with each other in a certain return period. The characteristics of rainfall are different in different geographical areas, and there are many types of rainfall, even in the same area. Urban drainage and stormwater management systems are designed according to different return periods.
Figure 1 shows the relationship between rainfall intensities and duration under different return periods according to the recommended rainfall formula in the Local standard of Beijing municipality: Code for the design of stormwater management and harvest engineering [
20]. It can be seen that rain intensity changes with the duration at every return period, the shorter the duration, the greater the rainfall intensity. In order to improve the simulation accuracy of the hydrological model based on the SCS-CN model and to provide the scientific basis for the planning and design of flood control, it is necessary to study the influences of rainfall intensities and duration on the parameters of the model.
Therefore, in order to study the effects of different rainfall intensities and duration on the model parameters (S/CN and λ), we carried out simulated rainfall experiments on simulated sloped runoff plots and obtain synchronized records of rainfall and runoff under three types of rainfall intensity and duration. We calculated S and λ every ten minutes by the general model fitting and event analysis methods using rainfall and runoff synchronized data. The parameter calculated and the parameters obtained using Fu et al.’s method were evaluated using three statistics (the Nash–Sutcliffe efficiency (NSE), the percentage deviation coefficient (PBIAS) and the ratio of the root mean square error to the standard deviation of measured data (RSR)). In the end, we give a discussion on the effects of rainfall intensities and duration on the model parameter values.
3. Materials and Methods
3.1. Simulated Rainfall System
This study was carried out in Beijing Forestry University simulated rainfall hall, located in Jiufeng National Forest Park. The simulated rainfall system specially developed for scientific research experiments was made by Xian Qingyuan Co. (Xi’an, China). The simulated rainfall system is not restricted by nature, and the rainfall and duration can be adjusted. Several investigators [
21,
22] have conducted various runoff and erosion experiments using this system. This system includes three parts: a rainfall system, control system and water supply system. The rainfall process can be automatically or manually controlled. The nozzle of the artificial rainfall system is a rotary down spraying nozzle developed by Spraying Systems Co. (Glendale Heights, IL, USA). The superimposed nozzle method is used to simulate natural rainfall. The rainfall uniformity is above 85%. The nozzle height is 12 m, so the raindrop can reach terminal velocity. This system is equipped with a highly sensitive rain gauge, so the rainfall intensity can be measured in real time and precisely controlled.
3.2. Runoff Plots
The runoff plots were formed through placing soil into steel tanks. The tank’s dimensions were 2 × 0.5 × 0.3 m. There were two runoff plots, one for calibration, the other for validation. The plot slope can be adjusted through a gradient adjustment device under the steel tank. In this study, we set the slope to 10 degree. A collecting bucket was installed at the lower terminal to collect the runoff.
The soil was taken from farmland in Changping, Beijing, which is cinnamon soil, one of the typical soils in this area. The soil bulk density was 1.31 g/cm
3 with an organic content of 1.5%. The distribution of the soil particles is shown in
Table 1. The soil type belongs to B in NEH-630. The soil was sieved through a 10 mm soil sieve. The tank was filled with the soil evenly layer by layer with soil bulk density controlled at 1.31 g/cm
3. The soil moisture content was controlled at 28% before the experiment.
The main experimental factors are shown in
Table 2. The type of land use was pasture, and the vegetation used in our experiment was
Festucaelata which is typical in North China. The vegetation coverage was about 60%. The planting method was transplantation, with the planting row vertical to the plot slope. Grass purchased was planted with a row width 30 cm and a row spacing 20 cm. After planted, the grass was cured until it grew new roots and fully resumed.
The experiments were carried out from June to August, the experiment time interval was 7–8 days. The antecedent moisture condition (AMC) is divided into three conditions (AMCI, AMCII and AMCIII). According to the results of research by Fu et al. [
6] on
CN values in the Beijing area, this experimental condition was assigned to AMCI.
3.3. Experiments and Data Collection
Through the rainfall intensity–duration–frequency diagram of Beijing (
Figure 1), we chose 30, 60, 90 mm/h intensities as experiment rainfall intensities. The total rainfall was 90 mm, and the rainfall type was uniform. A total of 3 replicates were performed for each intensity of rainfall.
Before the experiment, a bucket was placed under the collecting tank to receive the runoff. The start of the simulated rainfall was recorded as the beginning time of the rainfall, and the time when the runoff begins was recorded as the runoff beginning time. After the runoff beginning, the bucket that had been placed under the collecting tank was substituted with an empty bucket constantly. Within the first 20 min, the substituting interval was 2 min; 20 min later, the interval was changed to 5 min; after 1 h, the interval was changed to 10 min. After each replacement, the replaced bucket was placed in the idle position at the rainfall hall in the order of substitute. After the rainfall was over, runoff in the buckets was measured and recorded.
3.4. Runoff Intensity and Runoff Volume Caculating Method
Through
Section 3.3, we obtained the synchronized break-point data of runoff. The runoff amount was obtained by adding up the collected runoff. The runoff depth was equal to runoff amount divided by runoff area. The runoff intensity was the runoff depth every minute, calculated by dividing the runoff depth versus the time the runoff was used.
3.5. Calculation Methods of the Mode’s Parameters
The calculation methods used in this study for the parameters were the general model fitting method and the event analysis method. These methods are the same as used by Woodward [
23]. In order to examine the influence of the duration on the parameters, the parameters were calculated every ten minutes under different rainfall intensities. Firstly,
Ia was defined as the cumulative rainfall from the beginning of the rainfall to the beginning of runoff, rainfall
P was defined as the cumulative rainfall from the beginning of the rainfall to the interval time, runoff
Q was defined as the cumulative runoff from the beginning of the runoff to the corresponding interval time.
(1). General model fitting
The object was finding
λ and
S of Equation (5) using iterative least squares procedure fitting, which made:
the minimum. For the interval data of rainfall
P and runoff
Q, the parameters meet: R
2 > 0.5.
(2). Event analysis
The S was calculated by putting Ia, P, and Q into the Equation (4), and λ equals Ia/S. The average of these values of the replicates was taken as the parameters required.
(3). Fu et al.’s methods
Fu et al. used this method to obtain the
CN values in the Beijing area. The method is based on the standardized procedure in NEH-630. The initial abstraction ratio is regarded as a constant of 0.2. The
S for a rainfall event in a runoff plot is calculated using the equation:
The calculated S is converted to the corresponding CN value using Equation (6). According to the antecedent precipitation index (API), most AMC in the Beijing area belongs to AMCI (Fu et al.). Therefor the average of these CN values is taken as the runoff plot CN1 value. The AMC in this study belonged to the same condition, and we used this method to obtain CN1 value to evaluate the parameters based on rainfall intensities and duration.
3.6. Evaluating Statistics
After determining the parameters using the above methods, the Nash–Sutcliffe efficiency coefficient (NSE), the percentage deviation coefficient (PBIAS), and the ratio of the root mean square error to the standard deviation of measured data (RSR) were used to evaluate the model parameters. The NSE closer to 1 indicates that the predicted values are closer to the measured values, the better the prediction is; when the NSE is equal to 0, the predicted values are equivalent to the measured average value, and the predicted values less than 0 are less accurate than the measured average value [
24]. The PBIAS is used to measure the relative magnitude of the predicted values and the measured values. The positive values indicate that the predicted values are smaller than the measured values, while the negative values indicates that the predicted values are greater than the measured values [
25]. RSR is the ratio of the mean square error of the measured values to the predicted values and the mean square error of the measured values itself. This study used the standards recommended by Moriasi et al. [
26], which are NSE > 0.50, PBIAS ± 25% and RSR ≤ 0.70. These statistics were computed using the following formulas:
where
is the runoff depth for the
ith rainfall event, mm;
is the runoff depth calculated for the
ith rainfall event, mm,
is the simulated runoff average depth, mm, and
n is repeating time for validation.