The impact of rainfall value on the accuracy of the SCS-CN model: selection of model parameters

In the conventional approaches, λ is established as a constant value of 0.2 (Ajmal et al. 2020; Caletka et al. 2020). The CN value, as a dimensionless parameter, is employed to mirror the attributes of the underlying terrain in the basin prior to precipitation. These attributes are contingent upon soil type, antecedent soil moisture, land use, slope, and other determining factors. The CN values can be obtained from the relevant manuals, which take into account the soil type and other influencing factors. The primary advantage of the SCS-CN model is its reliance solely on CN values. However, this dependance results in a high sensitivity of the CN values (Golding et al. 1997), meaning that the SCS-CN model can only be adjusted for different research fields through changes in the CN value. Even slight variations in the CN value can lead to significant disparities in simulation outcomes. Therefore, numerous researchers have found that the traditional approaches exhibit limited precision in simulating complex systems.

In order to determine the AMC of a rainfall event used in a runoff prediction, 5-day antecedent rainfall (P5) was used as follows: AMC I if P5 < 35.56 mm in the growing season or P5 < 12.7 mm in the dormant season, AMC II if P5 between 35.56 and 53.34 mm in the growing season or 12.70–27.94 mm in the dormant season, and AMC III if P5 > 53.34 mm in the growing season or P5 > 27.94 mm in the dormant season (Kumar et al. 2021). However, there is no general agreement on the selection of rainfall values to determine the AMC level (Bhuyan et al. 2003; Thomas et al. 2021).

Currently, the research on the SCS-CN model mainly focuses on three points. First, the model is localized, and the empirical value is modified to a suitable value for a specific region. For example, da Silva Cruz et al. (2022) confirmed the CN value of the Amazon River Basin and forecasted the future flood situation of the basin. However, besides the CN value, λ is also an important empirical parameter affecting the value of the direct runoff. Consequently, some researchers have modified both λ and CN values to improve the accuracy of the SCS-CN model (Liu et al. 2021). Furthermore, this study showed that the model was applied to the study of runoff in urban areas. Owing to the limitations of the SCS-CN parameters, the model may not be able to complete the simulation task well in some research areas. Therefore, some researchers have focused on improving the model itself. For example, Walega et al. (2020) verified the accuracy of two improved SCS-CN models by comparing peak and direct runoff in three forestry areas in the southeast of the United States. These improved models can be understood as refinements of traditional models. They added a new parameter, early moisture M, in some complex conditions. Jiao et al. (2015) proposed a parameter of potential I_a to determine the maximum precipitation before the generation of runoff. This significantly improves the accuracy of the simulation compared to the traditional SCS-CN model. In addition, some researchers have integrated the SCS-CN model with the geographic information system (GIS) to expand the applicable scope of the model (Jethva et al. 2021; Saha et al. 2022).

The classical form of the SCS-CN model is represented by Equation (8). In the current model, P–I_a is utilized instead of P. In other words, the current model takes into account the influence of soil and other factors on runoff during rainfall and reflects the infiltration loss by means of λ. However, this does not imply that the infiltration losses are disregarded in the SWMM. On the contrary, the SWMM relies on surface permeability, sub-catchment areas, and other parameters input into the model to calculate the infiltration losses of the corresponding sub-catchment, rather than using a single parameter (Rossman & Huber 2016). In fact, the single λ will make I_a a fixed value that will cause errors in the prediction of the model results (Jiao et al. 2015). The simulations using the SWMM can avoid this phenomenon. Consequently, the simulation in the SWMM model merely focuses on the impact of the CN value on the runoff outcomes, without considering the influence of λ.

Another challenging issue lies in the quantity of data. In the case of the SCS-CN model and even some other studies related to rainfall–runoff, the quantity of data is typically several dozen or even fewer. This is because the surface rainfall–runoff data are challenging to measure, and it is not easy to guarantee the data quality due to factors such as terrain and vegetation. The second Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) is a reanalysis data product from The Global Modeling and Assimilation Office (GMAO) affiliated with the National Aeronautics and Space Administration (NASA). Reanalysis data products are based on the assimilation of a vast number of in situ and remote sensing observations into an atmospheric general circulation model and provide global, sub-daily estimates of atmospheric and land surface conditions across several decades (Reichle et al. 2017). In the regions lacking observations, significant advancements have been made in this field of MERRA-2 applications (Christensen et al. 2019; Baba et al. 2021; Ceppi et al. 2022).

In this study, the Nemor River Basin, located in the black soil region of northeastern China, is chosen as the research area. This basin is characterized by a flat terrain, exhibiting minimal topographical disparities among different regions, and the pattern of land use is dominated by cultivated land, which is suitable for employing the SCS-CN model. Therefore, it is necessary to conduct research on the model parameters for this study area. As mentioned above, when employing the SCS-CN model, the first step is to ascertain the empirical coefficient based on the characteristics of the study area, and further utilization of the model requires a more profound analysis. However, the limited number of study samples and the daily scale make an in-depth analysis challenging. Therefore, it is necessary to propose suitable parameters for the study region and determine the influence of λ and CN values on the SCS-CN model. The main purposes of this paper are to (1) determine the calculated and empirical values of CN and λ in the study area by analyzing the rainfall–runoff events, (2) investigate the influence of varying CN and λ combinations on the results of SCS-CN models, and (3) utilize the SWMM to validate runoff at a sub-daily time step and assess the impact of CN variations on the runoff curve.

The research region was the Nemor River Basin, with an area of 377.52 km², located in Nehe City at 125.5°E 48.0°N (Figure 1). The study region is located in the hilly transitional zone between the Lesser Khingan Mountains and Songnen Plain. The terrain is high in the east and low in the west. The Nemor River flows from west to east, passing through Nehe City and merging into the Nenjiang River. The annual precipitation is 500–600 mm, and rainfall normally occurs from July to September each year. One challenge in runoff analysis lies in the quantity of data. Owing to the difficulties associated with monitoring, the amount of data is restricted and the quality is rather inferior. Therefore, this study combines the runoff plot data and reanalysis data. The reanalysis data are from MERRA-2 (GMAO 2015a,,2015b, 2015c), which has an accuracy of 0.625 × 0.5°. The values in the dataset represent the average values within the region. The runoff plot data were collected from the runoff plot at the Keshan Farm weather station (125°23′8″E 48°18′35″N). The Keshan Farm is situated at the basin outlet. This dataset is employed to represent the runoff measurements within the basin.

The study region is in a cool climate zone, characterized by drought and wind in spring, high temperature and rain in summer, rapid cooling in autumn with an early frost period, and a long and snowy winter, which is cold and dry. The annual average temperature has been 3 °C, reaching 2.1 °C in the past decade. The extreme maximum temperature can reach 31 °C, and the minimum temperature can reach −30 °C. The final frost period was mid-May, the first frost period was mid-September, and the frost-free period lasted ∼120 days. The annual precipitation was ∼203.9 mm in the previous year, accounting for 43.8% of the total precipitation from May to September. The rainfall distribution accounted for 30.2, 45.8, 24, and 0.04% in spring, summer, autumn, and winter, respectively. Because of the high proportion of agricultural land, the Nemor basin is an important grain production base in Northeast China, with soybeans, corn, and potatoes as the main crops. In some farms of the basin, non-urban land, such as cultivated and forested land, accounts for nearly 90% of the total land area (Xing 2017).

Table 1 shows the sources of the data used in this study. The meteorological data obtained by reanalysis data come from the atmospheric reanalysis dataset of MERRA-2, whose rainfall data have been shown to perform well in the Hulunbuir region, which is adjacent to the study area (Qu et al. 2022). In addition to the reanalysis dataset, the data of the runoff plot in the Keshan Farm weather station were selected as the supplementary verification (Table 2). The runoff plot of the weather station is located at the drainage outlet of the basin. Owing to the long winters in the study region, the precipitation data from May to October every year were selected for this study to exclude the impact of snowfall. We selected 27 precipitation events from 2020 to 2022 as model parameters. The selection of precipitation events should meet the following criteria (Hawkins et al. 2002): (1) storm events that exclude discontinuous precipitation; (2) the peak flow rate of the process line should be higher than 0.2 m³/s; (3) small precipitation incidents were removed, and the antecedent runoff condition in the watershed should be average or higher, correspondingly ARC II or III. This was to avoid the influence of small storms on the deviation of high curves. (4) Uniform spatial distribution of precipitation within the watershed.

The relationship between average annual permeability and rainfall can be obtained from multiyear rainfall–runoff data in the research region. The runoff component can then be used to determine the relationship between I_a in this watershed and runoff. Next, Equation (3) was utilized to calculate the λ values of each event correspondingly to each event and then obtain a representative λ according to the arithmetic average method. The arithmetic average method was also used to calculate the CN values. The main steps were to calculate the corresponding S-value to each measured rainfall and runoff data point according to Equation (4), then calculate the CN value corresponding to each S -value from Equation (5), and then average the CN value. The CN value calculated using the average arithmetic value was taken as the suitable value. Two modeling methods were used as follows. To compare the accuracy between the SCS-CN model with new parameters and the empirical parameters, two methods were used as follows:

• Method (1): The SCS-CN model with the calculated λ and CN values.

• Method (2): The SCS-CN model with empirical λ and CN values.

In SWMM modeling, the process is as follows: First, the input and processed digital elevation model (DEM) data from ArcGIS were used to divide the sub-catchments and obtain the area and average slope. Subsequently, according to the data on soil type and land use, the parameters, including Manning and permeability coefficients in the area, were specified. The CN value used in the calculated value method is obtained by calculating the rainfall value. The empirical value method derives the CN value based on geographical information and rainfall conditions.

The study region demonstrates that F accounts for approximately 75.9% of the average rainfall, as calculated. Thus, Equation (1) determined that the relationship between the I_a of the watershed and the rainfall–runoff is I_a = 0.241P-Q. The I_a and S values corresponding to each rainfall event were derived based on the rainfall–runoff data collected during the study period. According to the analysis of 27 rainstorm events based on the rainfall–runoff process, it was observed that there existed variations in the λ value among different rainstorms within the watershed, with a majority of values being concentrated around 0.02. Among these values, the minimum was 0.011, the maximum was 0.021, the mean was 0.019, and the median was 0.020, respectively. The λ value remained unaffected by the rainfall; thus, the final value of λ was 0.02, consistent with that reported by Ajmal et al. (2015).

Method (2) is an empirical value method where λ is 0.2. The CN value refers to the experienced manual (Gironás et al. 2010) and the research results of other researchers (Jiang 2017; Xiuquan & Haoming 2019), taking into account that 90% of the research region is black soil farmland with an empirical value of 82.

Six rainfall events from the monitoring plot were used, and the information is shown in Table 2. For this set of data, the CN is calculated using the same method mentioned above. The results showed the mean of CN 72, which is in proximity to the result calculated from the reanalysis dataset. It can also be observed that when λ is set as 0.2 to calculate the CN value, there is a significant difference between this value and the one calculated according to the reanalysis data. Particularly, when the CN value is in small rainfall events (with rainfall less than 30 mm), runoff should not be generated. Hence, the value of λ should be 0.02.

It is evident that there is a significant difference between the model results calculated for all events and those excluding heavy rainfall events (p < 0.05), suggesting that heavy rainfall events enhance the accuracy of the model. Furthermore, heavy rainfall events appear to have a more substantial positive impact on the accuracy of the empirical value model. In other words, for predicting heavy rainfall events, using the empirical value model with a higher CN value yields more accurate results.

In the validation of the daily and the sub-daily steps, it can be observed that the result of the calculated value model typically exhibits superior performance compared to the empirical one. However, particularly as the amount of rainfall increases, the calculated value model demonstrates a poor performance in some of the events. More profoundly, this phenomenon indicates that the accuracy of the model depends not only on the CN and λ but also on the rainfall value.

In moderate rainfall events, the SWMM model with a high CN value demonstrates good performance during the initial rainfall period. However, as the rainfall progresses, the decline in runoff values is not in a regular pattern. The reasons for this can be inferred from the daily time step simulation. Under the high CN value, the SCS-CN model exhibits inaccuracies in estimating surface infiltration during light rain events and tends to overestimate runoff, resulting in higher values than actual measurements. Even though the SCS-CN model may provide accurate results for a rainfall intensity of 20 mm, its performance is compromised when considering inter-catchment influences within SWMM. Particularly under continuous rainfall conditions, the model's calculations quickly saturate the surface soil, leading to significant errors. For the simulation of heavy rain events, it is rather challenging to assess which model performs better, as the performance of the models differs in response to various rainfall events. Therefore, under certain CN values, the model may overestimate the runoff of light rainfall events, but the prediction for heavy rainfall events may be accurate. In other words, the SCS-CN method often performs poorly in the simulations of continuous rainfall because the CN value treats the model's flow-producing capacity as a fixed value, but as the rainfall continues, its flow-producing capacity decreases with the saturation of water in the soil, resulting in an error. In fact, the same problem exists with daily rainfall (Grimaldi et al. 2013; Ogden et al. 2017; Wang & Chu 2023). This implies that different CN values should be selected according to the rainfall amount rather than a fixed value. Therefore, on the basis of the events selected in Section 3.1, we calculated the CN values corresponding to all events during the period from 2020 to 2022. Moreover, these CN values were fitted via nonlinear regression analysis.

It can be seen from the figure that as the rainfall value increases, the CN value does not increase monotonically. At values below 16.3 mm, the CN value demonstrates a decreasing tendency as the rainfall amount rises. However, beyond 16.3 mm, the CN value ascends with the increase in rainfall. The pattern accounts for why the calculated value model performed relatively well in the rainfall event of 67 mm but underestimated the runoff in the heavy rainfall event of 84 mm. Even both models show such a result (Figure 10) since an overly large rainfall amount demands a larger CN value for the model. Similarly, the situation also occurs in the result of the runoff plot dataset. Although the CN value calculated from the monitoring point is generally higher than that obtained from the reanalysis dataset, the variation law still exhibits the same trend with the increase in rainfall. The Nemor River Basin has an evenly distributed rainfall and a flat terrain, lacking topographies such as valleys and hills that can significantly affect surface runoff. Therefore, in the process of using the SCS-CN model to predict runoff, the regional average CN value assumes a crucial role. Consequently, the CN value must be accurately determined rather than simply using a fixed value for a simplistic generalization.

Determining CN and λ is the prerequisite of applying the SCS-CN model, and understanding how CN and λ influence the model outcomes is also a prerequisite for enhancing the model. In this study, the calculated CN value of 67 and λ value of 0.02 from the rainfall–runoff events are optimal for the study region as they provide much higher accuracy than the results obtained under the empirical method with CN value of 82 and λ value of 0.2. This study also reveals the influence of parameter selection on the predicted values of the model. Regarding λ, a large λ will result in a smaller outcome than a small λ. Concerning the selection of the CN value, it should be determined in accordance with the rainfall condition. Within the study area of this research, the CN value of the model exhibits a pattern that initially decreases and subsequently increases with the augmentation of rainfall. Therefore, it is imperative to consider the impact of their combination, and the selection of the CN value should refer to the most representative rainfall event within the study period. Another contribution of this paper lies in the combination of measured data and reanalysis data. The conclusions drawn from the two datasets are largely consistent. This indicates that the reanalysis dataset performs in accordance with the actual law under the SCS-CN model, providing a foundation for its further utilization. We hold the opinion that AMC, slope, and other factors that determine the CN value might also have the potential to serve as thresholds, which could be the subject of future research.

Conceptualized by J.L. and Q.S.; developed the methodology by J.L.; software of J.L.; validated by J.L., Q.S.; rendered support in formal analysis of J.L.; investigated by J.L.; resources of Q.S.; rendered support in data curation of J.L.; wrote the original draft preparation by J.L.; wrote the review and edited the article by Q.S.; visualized by J.L.; supervised by Q.S.; performed the project administration by Q.S. All authors have read and agreed to the published version of the manuscript.’

This research was funded by the National Key Research and Development Program of China (2021YFD150060102).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.