Abstract
The United States Natural Resources Conservation Services Curve Number (NRCSCN) method uses the CN and rainfall to calculate runoff. However, there are still some uncertainties in the method, such as choosing the most appropriate CN value. Therefore, this study attempts to evaluate the effectiveness of using the NRCSCN method to estimate the runoff of five catchments in Sudan. For each catchment, CN values were obtained from the number of observed rainfallrunoff events using the NRCS table, arithmetic mean, median, and geometric mean methods. For each method, Nash–Sutcliffe efficiency (NSE) was obtained to evaluate the fit between the observed and runoff, and negative NSE values were found for all methods. Negative values of NSE indicate that the observed runoff and estimated runoff are not well fitted, and the NRCSCN method is not suitable for runoff calculation in the study areas.
1 Introduction
Runoff estimation from rainfall is of great significance in flood control research. In addition, direct runoff estimates are important for power generation, agriculture, and irrigation in a lot of countries [1]. There are various ways to estimate runoff. The Soil Conservation Service Curve Number (SCSCN) method is the most commonly used method for estimating runoff, and it was renamed as the Natural Resources Conservation Services Act (NRCS) in 1994 [2]. CN tables were developed by the United States Department of Agriculture. CN usually ranges between 30 and 10 [3]. Low runoff is represented by minimum values of CN, while CN values approaching 100 represent high runoff. The United States Department of Agriculture developed this method; it relies on land use and land cover types of the American agricultural catchments. The characteristics of land use and land cover in Sudan are likely to be different from those in the United States. Land use, soil type, antecedent water conditions, treatment, and surface conditions are the main factors affecting runoff generation. The disadvantages of the NRCSCN method include a single parameter containing a variety of factors (such as land use, soil type, antecedent water condition, and surface conditions) rendering the method very delicate, the influence of spatial scale, intensity, and temporal distribution of rainfall and the effect of adjacent moisture condition are not considered [2]. In general, the Sudan curve numbers are obtained from the NRCSCN tables, and the curve numbers in these tables may not be applicable to Sudan, as the NRCSCN tables depend on the land features of the United States. In this article, the authors attempt to evaluate the use of the NRCSCN method to estimate runoff in five catchments in Sudan. Using NRCSCN tables, CN values were estimated in a Geographic Information System (GIS) [4]. Shuttle Radar Topography Mission 30m resolution (SRTM30) is the Digital Elevation Model (DEM) used in this research [5]. Rainfallrunoff events were used to calculate the CN using three statistical methods (arithmetic mean, median, and geometric mean).
2 Methods
2.1 Study area
The study areas are distributed in different parts of Sudan. The first study area is the Abufargha catchment in the eastern region of Sudan in Al Gadarif State (Figure 1a). Abufargha catchment has a drainage area of 92.4 km^{2} and its outlet coordinates are 14°02′ N and 35°22′ E. The second study area is the Eldilling catchment in the southern region of Sudan in South Kordofan State (Figure 1b). The Eldilling catchment has a drainage area of 484.84 km^{2} and its outlet coordinates are 13°11′ N and 29°59′ E. The third study area is the Erigi catchment in the western region of Sudan in North Darfor State (Figure 1c). The Erigi catchment has a drainage area of 73.3 km^{2} and its outlet coordinates are 14°00′ N and 24°31′ E. The fourth study area is the Tiflo catchment in the western region of Sudan in North Darfor State (Figure 1d). The Tiflo catchment has a drainage area of 329.87 km^{2} and its outlet coordinates are 14°24′ N and 23°32′ E. The last one is the Abasya catchment in the southern region of Sudan in South Kordofan State (Figure 1e).” The Abasya catchment has a drainage area of 289.23 km^{2} and its outlet coordinates are 12°10′ N and 31°19′ E. The DEM is a fundamental dataset for the simulation of the stream network; it is useful for the delineation of the watershed and the illustration of the topographic variations in the area. In this study, the DEM with 30 m horizontal spatial resolution was used, mosaicked, and processed.
Figure 1
3 Data sets
Daily rainfallrunoff events from five catchments were obtained from Sudan Meteorological Authority and Ministry of Water Resources, Irrigation, and Electricity. Each of the catchment’s daily events were used to estimate the CN. Measuring stations at each catchment outlet were used to measure runoff. Daily rainfall and runoff were measured in millimeter (mm) units. Thiessen Polygon method was used to represent the average rainfall over study areas. In this study, events having runoff coefficients greater than 1% were used. The number of events for Abufargha, Eldilling, Erigi, Tiflo, and Abasya catchments is 24, 28, 36, 17, and 18, respectively. The period of daily events for the Abufargha catchment is from 1981 to 2008, from 1974 to 1986 for Eldilling catchment, from 1966 to 1975 for Erigi catchment, from 1965 to 1973 for Tiflo catchment, and from 1968 to 1973 for the Abasya catchment.
4 Curve number estimation
4.1 CN estimation using NRCSCN tables
To estimate CN using NRCSCN tables, Arcmap 10.5 was used. The common estimation method of NRCSCN by using Arcmap 10.5 is as follows:
Selection and drawing of the outlines of the catchments.
Determination of the catchment areas.
Mapping of the soil types and land use for catchment areas.
Changing of the soil types to hydrologic soil groups.
Overlaying of the land use and hydrologic soil group maps to identify each unique land use, soil group polygon, and to compute the area of each polygon.
Allocation of a CN to each singular polygon based on the NRCSCN tables [6].
The total CN of the catchment is calculated by area weighting of the polygons of the land usesoil group in the catchment.
5 NRCSCN estimation from daily rainfall and runoff data
The formula for estimating runoff depth using NRCSCN is as follows:
where P is the depth of rainfall (mm), Q is the depth of runoff (mm), and S is the potential maximum storage [7]. The general equation of NRCSCN is given by:
where P is the depth of rainfall (mm), Q is the depth of runoff (mm), λ is the initial abstraction (Ia) coefficient, and S is potential maximum storage [2]. By knowing the rainfall and runoff data in the catchments, CN is estimated by applying equations (3) and (4). Considering λ to be equal to 0.2, equation (3) will be [8]:
CN is estimated from S:
Arithmetic mean [9], the median, and geometric mean [10] were used to obtain CN values from rainfallrunoff data.
The depths of rainfall and runoff are substituted into equation (4) to obtain the values of the computed and measured S. When S is substituted into equation (5), the computed and measured CN can be obtained. Equation (6) was used to obtain the CN using the geometric mean method.
5.1 Statistical analyses
The coefficient of determination (R ^{2}), the NSE, and percentage mean bias (PBIAS) were utilized for the statistical analyses. R ^{2}, NSE, and PBIAS were computed using equations (7)–(9) [11].
where
If R ^{2} is greater than 0.5, it is considered “acceptable.” NSE values range from −∞ to 1, and can be considered as “very good” if 0.75 < NSE ≤1; “good,” if 0.65 < NSE ≤75; “satisfactory,” if 0.50 <NSE ≤0.65; and “unsatisfactory,” if NSE ≤0.50. The PBIAS positive and negative values indicate model underestimation bias. The PBIAS can be considered “very good” if PBIAS < ±10%; “good,” if 10% ≤ PBIAS < ±15%; “satisfactory,” if 15% ≤ PBIAS < ±25%; and “unsatisfactory,” if PBIAS ≥ ±25% [11].
6 Results and discussion
In order to generate the CN based on NRCSCN tables, soil maps, land use maps, and hydrological soil maps were prepared. The results are as described below:
6.1 Hydrological soil map
For each catchment, the generated hydrologic soil group was used as the input of the CN in ArcMap 10.5. It is a feature of the soil mapping unit and each soil mapping unit is allocated to a particular hydrological group: A, B, C, and D [10]. The watershed has different soil groups according to which the soil code has been assigned. Clay loam was taken as hydrologic group D, sandy clay loam as soil group C, loam as soil group B, and sandy loam as hydrologic group A. The hydrologic groups A, B, C, and D formed in Arcmap 10.5 are shown in Table 1 and Figure 2(a)–(e). Due to different infiltration rates, each soil group has different runoff. The soil in group A has the lowest runoff potential, while the soil in group D has the highest runoff potential [12].
Table 1
Catchment  Hydro group  Area (%) 

Abufargha  C  100 
Eldilling  A  22.4 
C  0.76  
D  76.9  
Erigi  A  97.7 
B  2.3  
Tiflo  B  100 
Abasya  C  4.6 
D  95.6 
Figure 2
6.2 Land cover maps
In the present study, the supervised classification was carried out in ArcMap 10.5. Two land use land cover grades such as residential and agricultural exist [4]. The land use land cover maps are shown in Table 2 and Figure 3(a)–(e).
Table 2
Catchment  Land use  Area (%)  Land use reclassification 

Abufargha  Croplands  86.9  Agricultural 
Cities  13.10  Medium residential  
Eldilling  Open deciduous Shrubland  4.70  Agricultural 
Closed grassland  0.32  Agricultural  
Cropland  1.67  Agricultural  
Crop with opened woody vegetation  93.31  Agricultural  
Erigi  Open grassland with sparse shrubs  15.90  Agricultural 
Cropland  84.10  Agricultural  
Tiflo  Open grassland  25.40  Agricultural 
Spare grassland  74.64  Agricultural  
Abasya  Open deciduous Shrubland  0.22  Agricultural 
Cropland  0.31  Agricultural  
Crop with opened woody vegetation  99.47  Agricultural 
Figure 3
6.3 Generating CN maps
The land use map, soil map, and the DEM as inputs are first imported into ArcMap 10.5. The HECGeoHMS extension tool of Arcmap 10.5 was used to generate the CN grid [12]. The appropriate code is given to the soil type. Soil code provides the hydrologic soil group in the area. Then, the land use and hydrologic soil group are combined to form a new merged soil and land use map. The CN look up table (Table 3) was created and the appropriate CN value was assigned for each soil land map [13]. The CN values for each catchment using the NRCSCN tables are shown in Table 3 and Figure 4(a)–(e).
Table 3
Land use  A  B  C  D 

Medium residential  57  72  81  86 
Agricultural  66  77  78  87 
Figure 4
6.4 CN estimation using rainfall and runoff data
For each catchment, rainfallrunoff events were analyzed and the CN values, R ^{2}, NSE, and PBIAS were estimated for five catchments as shown in Table 4. CN values for the Abufargha, Eldilling, Erigi, Tiflo, and Abasya catchments range from 82.94 (NRCSCN table) to 90.96 (geometric mean), from 82.43 (NRCSCN table) to 87.19 (median), from 67.13 (NRCSCN table) to 93.11 (geometric mean), from 77 (NRCSCN table) to 94.63 (median), and 86.597 (NRCSCN table) to 98.71 (geometric mean), respectively. R ^{2} for Abufargha, Eldilling, Erigi, Tiflo, and Abasya catchments are 0.575–0.621, 0.509–0.5533, 0.239–0.625, 0.061–0.746, and 0.5368–0.632, respectively. NSE values for Abufargha, Eldilling, Erigi, Tiflo, and Abasya catchments are −2.941 to −20.441, −21.655 to −38.1557, −2.365 to −6.874, −161.937 to −1846.635, and −522.935 to −2763.9, respectively. The PBIAS for Abufargha, Eldilling, Erigi, Tiflo, and Abasya catchments are 217.565–400.011, 459.040–8599.886, 281.614–1614.411, 1194.876–1903.735, and 1149.784–2660.558, respectively.
Table 4
Catchment  Method  CN  R ^{2}  NSE  PBIAS (%) 

Abufargha  NRCS table  82.94  0.575  −20.441  217.565 
Arithmetic mean  87.88  0.619  −3.441  303.380  
Median  87.54  0.621  −2.941  294.978  
Geometric mean  90.96  0.598  −10.977  400.011  
Eldilling  NRCS table  82.43  0.509  −21.655  459.040 
Arithmetic mean  83.12  0.5197  −24.543  85.999  
Median  87.19  0.5533  −38.1557  583.051  
Geometric mean  87.18  0.5533  −38.1152  582.755  
Erigi  NRCS table  67.13  0.239  −2.958  281.614 
Arithmetic mean  90.74  0.625  −2.989  295.482  
Median  91.19  0.624  −2.365  281.3296  
Geometric mean  93.11  0.619  −6.874  1,614.411  
Tiflo  NRCS table  77  0.061  −161.937  1,194.876 
Arithmetic mean  90.50  0.689  −883.373  1,358.468  
Median  94.63  0.746  −1,846.635  1,903.735  
Geometric mean  93.90  0.736  −1,604.722  1,767.090  
Abasya  NRCS table  86.597  0.5368  −522.935  1,149.784 
Arithmetic mean  90.06  0.565  −801.583  1,284.274  
Median  95.43  0.603  −1,698.02  1,823.094  
Geometric mean  98.71  0.632  −2,763.9  2,660.558 
It is noted that NSE values of the five catchments are all negative. These negative values indicate the difference between the observed and estimated runoff (poor fit). Previous studies have shown that SCSCN has poor performance in areas with high infiltration rates, such as areas with predominant sand soils [14]. The literature review has also revealed that λ the initial abstraction (Ia) coefficient may not be equal to 0.2 [7], which would affect the fit between the observed and estimated runoff. All the values of PBIAS were positive, indicating that runoff was underestimated [15,16,17,18]. Except for the NRCS table method for the Erigi and Tiflo catchments, all methods have R ^{2} value greater than 0.5. This result shows the significance of prospective studies on the use of the CN method in the Sudanese catchments, such as the one developed in this study [19,20,21,22,23,24,25]. The author recommends measuring the initial abstraction (Ia) to understand the actual value of initial abstraction coefficient (λ) to know the actual value of λ. The initial abstraction coefficient (λ) will affect the fit between the observed and estimated runoff, because some previous studies have shown that λ may not be equal to 0.2 [26,27,28,29,30,31].
7 Conclusion
There are still some uncertainties in the (NRCSCN) method, such as choosing the most appropriate CN value. This study aimed to evaluate using the NRCSCN method to estimate the runoff of five catchments in Sudan. The first study area is the Abufargha catchment in the eastern region of Sudan. The second study area is the Eldilling catchment in the southern region of Sudan, the third study area is the Erigi catchment in the western region of Sudan, the fourth study area is the Tiflo catchment in the western region of Sudan, and the last one is the Abasya catchment in the southern region of Sudan. For each catchment, CN values were obtained from the number of observed rainfallrunoff events using the NRCS table, arithmetic mean, median, and geometric mean methods. The R ^{2}, the NSE, and PBIAS were utilized for the statistical analysis. R ^{2}, NSE, and PBIAS were computed for five catchments. NSE values of the five catchments are all negative. These negative values indicate the difference between the observed and estimated runoff and the NRCSCN method is not suitable for runoff calculation in the study areas.
Acknowledgements
This study was supported by School of Water Resources and Environment, China university of Geosciences (Beijing). The authors are very grateful to Suzan Mustafa (Ministry of Water Resources, Irrigation, and ElectricityKhartoum, Sudan) for her support and guidance during the study.

Author contributions: Salma Ibrahim and Babikir Barsi conceived the presented idea. Salma Ibrahim and Magdi Siddig collected the data. Salma Ibrahim developed the theory and performed the computations. Salma Ibrahim, Babikir Barsi, and Qingchun Yu verified the analytical methods. Salma Ibrahim wrote the manuscript with support from Babikir Barsi, Qingchun Yu, and Magdi Siddig. All authors have agreed to the final manuscript.

Conflict of interest: Authors state no conflict of interest.
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