Curve Number Estimation for Ungauged Watershed in Semi- Arid Region

The Benanain Watershed is located in East Nusa Tenggara with an area of 3,181 km and is divided into 29 subwatersheds. The East Nusa Tenggara itself is an eastern region of Indonesia with a unique climate condition called semiarid. The high rainfall intensity occurring in short duration results in large surface runoff and erosion. Floods and erosion in semi-arid areas due to sensitive soils to drought and heavy rainfall extremely. This paper presents the application of the Soil Conservation Services-Curve Number (SCS-CN) real-flood flows through a digital map of soil type, land use, topography, and the heterogeneity of physical condition, especially for ungauged watersheds. The method used is an approach empirical to estimate runoff from the relationship between rainfall, land use, and soil hydrology groups. This watershed has a large area that must analyze every sub-watershed. The land-use of the Benanain watershed is secondary dryland forest by 44.26% and the hydrological soil group on the B group classification with medium to high absorption potential by 46.502% from the total area. The curve number value of the Benanain Watershed ranges from 56.54 to 73.90, where the mean CN value of 65.32. The rainfall (mm) for the 29 sub-watersheds in the Benanain Watershed has decreased by about 74.65% when being surface runoff or only 25.35% of water becomes surface runoff. The relationship between rainfall depth and CN is classified as standard response and trend line (flat slope) equilibrium occurs when rainfall depth value of 56.71 mm and CN is close to 66.30. The high variability of intense rainfall between the rainy season and the dry season had a significant influence on the curve number value in a large watershed area. Further analysis will be more accurate if it is supported by long rainfall data and observation runoff data as a control.


Introduction
A semi-arid region is an area that receives lower rainfall compared to potential evapotranspiration. This semi-arid region covers 31% of the world's [1]. The climate in East Nusa Tenggara (NTT) is of type D with the rainy season (average of monthly rainfall > 200 mm) that occurred between 3-4 months [2]. The characteristic of semi-arid regions is the evapotranspiration is much greater than precipitation, and the intensity of rainfall is very high during the rainy season. High-intensity rainfall variability during the rainy season and dry season causes enormous erosion [3,4]. The land surface temperature affected land use, land cover, vegetated areas, water resources, etc. [5]. East Nusa Tenggara which has semi-arid conditions, is of course also affected by the land surface temperature.
The large volume of rainfall exceeds the soil infiltration capacity resulting in a large of runoff and erosion. These extreme climatic conditions often lead to misinterpretation of rainfall data, especially in East Nusa Tenggara. That is because the rainfall does not spread evenly throughout the year [6]. The geographical form as thought watershed shape also has a big influence on rainfall. Large local storms can shed a large part of annual rain in just a few days or hours. That causes the river to experience massive flooding every year.
Flood modeling design is inseparable from the rainfall-runoff relationship, and one method that can use is the Natural Resources Conservation Service Curve Number (NRCS-CN). The advantage of this method was can used in areas where flood hydrograph data or automatic recording of water levels are not available; however, rainfall recording data are available [7]. Also, this NRCS-CN model selection be affected by several factors, such as: (1) a familiar model is used over the years around the world, (2) very efficient, (3) the required data input generally available, and (4) this model connecting runoff to soil type, land use and control practices [8].
NRCS-CN has several main elements in the rainfall-runoff process, such as watershed boundaries, rainfall, hydrological abstraction, and runoff [9]. Determination of curve number for watersheds characteristics that do not have flood hydrograph data and water level reservoir also can be seen from the watershed, namely soil type, land use, conditions hydrology, and antecedent moisture condition (AMC). NRCS-CN water loss method and the NRCS unit hydrograph also used to determine hydrologic soil groups from the Harmonized World Soil Database (HWSD) map. In this method, the runoff thickness or rainfall is a function of the total rainfall thickness and reflection parameter of the number of runoff curves called Curve Number [10].
Soil Conservation Services and Curve Number (SCS-CN) technique, also known as the Natural Resources Conservation Service Curve Number (NRCS-CN) is one of the simplest, and well-documented conceptual methods to predict rainfall-runoff. The SCS-CN model application was to estimate runoff from small watersheds and runoff processes typical of a watershed-based on a remote sensing geo-information [11]. The determination of the correction curve number value has been done in an oval watershed using the HEC-HMS model and influencing factors such as soil properties, geological formation, and land use [12].
The SCS-CN application in the Temef watershed shows that the soil hydrological group affects the flood water level [13]. The effect of river morphometric parameters on the potential for runoff in an ungauged river using satellite imagery, topographic maps, and rainfall data combined with geospatial techniques have been done by the previous [14]. The CN value can be used for comparative studies of the impact of urbanization and forest fires and their combined effect on the runoff response [15]. Estimating the curve number value use the SCS-CN method has been carried out by previous researchers because of its simplicity and practical design [18][19][20]. At present, many researchers use the GIS and Remote Sensing techniques to explore and analyze the curve number method in a small watershed [16,17,21]. The CN values also could be verified using a rainfall simulator confirmed by the statistical tests [22,23].
This study aims to determine a Curve Number (CN) value based on a hydrogeological map diversified to the hydrologic soil group map and check its applicability to the ungauged watershed such as in the Benanain Watershed. The characteristics of the Benanain watershed have very extreme fluctuation discharge, which indicates that the watershed is experiencing critical damage. Soil physical properties and land cover characteristics in semi-arid areas affect the value of curve numbers such as the Benanain watershed.

Soil Conservation Service-Curve Number (SCS-CN) Method
The Soil Conservation Services (SCS) method was developed from rainfall observation over many years and has involved many agricultural areas in the United States. This method attempts to relate watershed characteristics such as soil, vegetation, and land use with the curve number (CN), which shows the potential flow for a particular rainfall.
The CN method has based on the relationship between the infiltration of each soil type and the amount of rainfall that falls every time it rains. The CN values range between 1 and 100 that is a function of runoff resulting from soil types, land use, hydrological conditions, and antecedent moisture condition [10,16].
The form of the equation is: (1) Where Q = direct runoff (mm), P = rainfall depth/precipitation (mm), Ia = initial abstraction (Initial loss), and S = the water maximum retention potential by the soil, which a big part because of infiltration (mm).
The definition of initial loss is part of the rainfall used to wet the soil surface include plants, trash, and vacant land before the infiltration happened. For impermeable surface or cement coated, the initial loss is the amount needed to moisten the surface before water accumulates and becomes runoff. For forest land cover, lose initial is usually taken 5.1 -13 mm needed to wet the surface. Total this is rarely measured, and the SCS assumes that the initial loss is approaching 0.2 times the maximum soil moisture retention or S. Woodward et al. use 307 watersheds scattered in America, which has more than 20 flood events [24]. The results indicated a λ value of about 0.05 gives a better fit to the data and would be more appropriate for using the runoff simulations. That λ is not constant from watershed to watershed, and the assumption of λ = 0.20 is unusually high.
In determining the depth of excess rainfall or surface runoff, the correlation between Ia and S values shown as follows [7,17]: Based on Equation 3, the value of runoff depth (mm) is used in the following formula [20,25]: The maximum retention (S), and characteristics of the watershed associated with the intermediate parameter, namely Curve Number (CN).
Where CN (Curve Number) is a representation of potential runoff from the land cover -soil complex characteristics [10]. For watersheds with sub-watersheds that have a different land type and land cover, then CN composite values are determined based on: Where CNi is the CN value in the sub-watershed i, Ai is the area in sub-watershed i, and n is the number subwatershed. A combination of a hydrologic soil group, land use, and treatment class can be shown in Table 1 [8].
To estimate the curve number from rainfall-runoff data for S as a function of precipitation and depth runoff (Q) forms the equation [25]: (8) The strong relationship between CN and rainfall depth occurred when Equations 5 and 7 are used to calculate values of CN from observed rainfall depth and runoff depth. The CN method is often used as a transformation of design rainfall depth to design runoff depth for a given return period [25]. To determine the curve number for rainfall depth and runoff depth has been applied for an ungauged watershed in the Benanain River. Soil Conservation Services (SCS) has developed a soil classification system based on soil properties and classified it into four hydrological soil groups ( Table 2). Soil Conservation Services has developed a soil classification system based on soil properties and classified it into four hydrological soil groups ( Table 2). It is ranging from soil type A (very absorb water), B (potency absorbs moderately water), C (potency absorbs less water), and D (potency absorbs the least water). The definitions for each soil group adjusted by looking at the similarities to the potential surface runoff under the same weather conditions and land use. The depth and hydraulic conductivity of any water-impermeable layer and the depth to any high-water table, it used to determine the correct hydrologic soil group for the soil. Hydraulic conductivity is a quantitative measure of the ease with which water transmits through soil pores depending on the rock permeability. Lithological composition of rocks and permeability conditions to give qualitative information on the soil permeability, the occurrence of groundwater, and productivity of aquifers. It provides an overview of the depth of the aquifer (Table 3). Therefore, these two parameters are interrelated and linear relationship (the increases the hydraulic conductivity, the greater the permeability). Aquifers in which flow is through fissures, fractures, and channels: Moderately productive aquifers.
Aquifers in which flow is through fissures, fractures, and channels: Moderately productive aquifers.
Soil permeability was determined using the conversion of hydrogeological maps through to the Hydrological Soil Group maps [7] are shown in Table 4 and Table 5.

Figure 1. Benanain watershed in Timor Island
Malaka district is approximately 232 km from Kupang City to the east of Timor Island. This research was conducted in the Benanain watershed that flows to the estuary in the southeast of the Timor Sea. Figure 1 shows the changes in the shape of the river flow where there is a meander phenomenon. The river morphology has changed a lot. It has happened as a result of riverbank erosion which causes silting in the river channel. This sedimentation makes things worse if the flood intensity is high enough because the river cross-section was unable to accommodate the water flow.
The Malaka district has a tropical climate with an average temperature of 24 -34 °C. The maximum daily rainfall has varied between 16-68 mm in the eastern region, while 120-255 mm in most of the northern. The average annual rainfall has estimated at 1,500 mm/year [26]. This research used ten rainfall stations for ten years (1996-2008) and spread across four districts that crossed by the Benanain watershed. The average areal rainfall for the analyzed part of the catchment was determined using the Thiessen polygon method, as showed in Figure 2. The geographical location of rainfall stations shown in Table 6.  Land use activities in the Benanain watershed cause a change in the type of land cover, changes in vegetation, deforestation, shifting cultivation, converting forests to plantations, and changes in land management. The overflow in the Benanain River occurs almost every year and even repeatedly in a year. The flood tends to increase depending on the intensity of rainfall that occurs upstream. Therefore, it is necessary to the analysis of effects of land use and soil types on the curve number (CN) as one of the determining variables for discharge changes in the Benanain watershed. The characteristic of ten rainfall-runoff direct events for the analysis, with the calculated curve number according to Equations 4 and 6 presented in Table 7. The research flow chart to estimate the curve number model and to predict the amount of surface runoff is presented in Figure 3. The amount of runoff depth obtained in this study includes a rainfall depth (P) and the curve number prediction. Because the catchment area doesn't have observed runoff data, this study only estimates the curve number data from land use maps and soil maps. Furthermore, to determine the correlation between P and Q, Q and CN were done using statistical analysis.

Hydrological Soil Group Map
The Benanain watershed area has divided into 29 sub-watersheds (Figure 4), and based on the land use map for the island of Timor, the land cover types of the Benanain watershed can classify as in Table 8.

Figure 4. Land use map of Benanain watershed
It can be seen in Table 8 that the Benanain watershed has dominated by secondary dryland forest covering an area of 1,408.20 km 2 with CN values based on land use A = 25, B = 55, C = 70, and D = 77. Secondary dryland land forest in the Benanain watershed covers 44.26% of the total area, which means that is better than scrub or savanna. The secondary dryland forest has granular aggregates that are better at absorbing water. It has a scaly clay soil texture, moderate soil permeability, very poor soil porosity, moderately content weight, and low soil organic level content. The clay particles are more difficult to detach than sand or gravel, but clay is easier to transport. Hydrologic soil group (HSG) is determined by the water transmitting from the soil layer with the lowest saturated hydraulic conductivity and value of depth to the impermeable layer or a water table. A hydrogeological map gives complete information on the parameters needed for HSG determination as soil permeability, groundwater level position from the surface can use as the basis to determine the HSG value shown in Tables 4 and 5. Digitalization using ArcGIS based on the hydrogeological map of Timor Island obtained soil hydrological types and the groundwater level depth which divided into 19-types with low to very low, low to moderate, and moderate to high passing types with HSG B, C, and D ( Table 9). Determination of the Curve Number Value in the Benanain watershed using the SCS-CN method needs to be done by overlying (intersection) the hydrological soil group map and land use map. The results of intersection reclassification of land use maps and soil hydrology group maps are new polygons that represent the value of the curve number from the SCS. The result of the curve number value for 29 sub-watersheds in the Benanain watershed has shown in Table 9. The percentage of each soil type is tabulated in Table 8 to determine the dominance of soil types in the Benanain watershed. The sub-basin area that is classified as low to lowest (Type D) is 28,683%, low to moderate (Type C) is 24,815%, and the remaining moderate to high (Type) B is 46.502%. The lithology of soil types with the highest percentage is scaly clay containing boulders of other rock with low to very low permeability (the potential for water absorption is the least) has a value of 25.677%.
However, it can be seen in Table 9, based on the hydrologic soil group, the B group classification with medium to high absorption potential has a large area. It means water will absorb into the soil surface as infiltration by 46.502% of the watershed area when it rains. The classifications of hydrologic soil group in Benanain watershed with type C and D, which have medium to very low permeability indicate that most of the Benanain watershed has a potential for surface runoff. Soils in this group (Type C/D) have moderately to high runoff potential when thoroughly wet. Water movement through the soil is restricted or very restricted. Group D soils typically have greater than 40 % clay, less than 50 % sand, and have clayey textures.

Estimating Rainfall-Runoff
The runoff depth (Q) can be estimated using Equation 4 from the annual maximum daily rainfall data of 29 subwatersheds in the Benanain watershed presented in Table 10. Model validation should be done to examine the accuracy of the SCS Curve Number Method. However, because there is no observational runoff data in the study area, the design runoff can be assumed from the empirical relationship between the rainfall depth, curve number, and runoff depth. The relationship between rainfall depth (P) and runoff depth for the average of curve number 65.32 and has overlaid with the graphical solution of Equation 6 shown in Figure 6 [27]. The 29 pair runoff depth to rainfall depth is plotted and obtained relationship: With r 2 = 0.683 of CN = 65.32. Based on Equation 9, the increase in rainfall depth value by 7.03% will also affect the increase in runoff depth by 8.68 % for CN =65.32 in the Benanain watershed. Dots distribution shown in Figure 6 indicates a strong secondary relationship between rainfall depth vs. runoff depth for the mean of CN = 65.32. Hawkins [29] proposed to use an asymptotic function for the approximation of the relationship CN vs. rainfall depth values with the following equation: Where CN∞ is the constant values as P ∞; and k = fitting constant. Equation 10 was fitted using a least-square procedure for CN∞ and k. The fitting "k" can be following the equation: Where CN∞ = 100/ (1 + P/2) for P ∞ then CN (P)  100 k = CN∞ A standard asymptote occurs if there is a tendency for CN to decrease and then approach a constant value with increasing rainfall depth (mm) [25,28]. A similar trend was found for rainfall depth events and respective CN values as shown in Figure 7, considering P > 0.2 S and CN∞ = 100/ (1 + 50.8 P).
Where the values of the curve number are estimated from 56.54 -73.90 with the mean value equals 65.32. As there is a tendency for curve numbers to decrease with the increase of rainfall depth. Therefore, in the application of mean CN (65.32) for design floods estimation is not allowed. The trend line obtained on the Benanain watershed is similar to previous researchers [21,26], but the area study (watershed area) is smaller than this case. Hawkins (1993) suggests that the asymptotic line is a common and standard hydrological response to watershed behavior [29]. Therefore, in the Benanain watershed, the relationship between rainfall depth and CN is classified as a standard response. The asymptotic approach has the advantages that the more efficient use of the available data sources may be applied to ungauged watersheds and the results are similar to those derived from original data [30].
The average rainfall depth (mm) for the 29 sub-watersheds in the Benanain watershed has decreased by about 74.65% when being surface runoff depth. The runoff depth of the Benanain watershed may also be affected by landuse of the watershed (secondary dryland forest), river slope (0.45%) into the watershed, shallow soils (0.56 m), drainage density, and the confluence of tributaries so that the estuary is like a bottleneck. The equilibrium of trend line (flat slope) when rainfall depth value of 56.71 mm and CN approaches 66.30. The rainfall-runoff value that takes into account the curve number value in the Benanain watershed is also one of the factors that influence the flooding that occurs. The CN value in the Benanain watershed is in AMC I during the dry season, but a significant change will occur during the rainy season, where the CN value in the watershed becomes AMC III. Determination of CN value with a large watershed area and the high variability of rainfall intensity has a significant effect on the CN value, which results in the amount of surface runoff.
Analysis of the value of the curve numbers in the ungauged watershed is very helpful to estimate the percentage of water infiltration and water flow as surface runoff. Analysis of large catchment areas such as the Benanain watershed required mapping in smaller sub-watershed areas so that prediction data could be obtained closer to real conditions in the field. Therefore, it is necessary to conduct a similar investigation of the small watershed, with long rainfall records and observed runoff data, so calibration values can be obtained to flood frequency analysis.

Conclusion
The hydrological soil types in the Benanain watershed has classified into 19-types with three levels of permeability, namely, moderate to high permeability, moderate to low permeability, and low to very low permeability consisting of HSG B (moderate water absorption potential), HSG C (less water absorption potential) and HSG D (very less water absorption potential). The land-use type in the Benanain watershed is secondary dryland land forest covers 44.26% of the total area, which means that is better at absorbing water than shrub or savanna. Based on the hydrologic soil group, the B group classification with medium to high absorption potential reaches 46.502% of the total area of the Benanain watershed. It means water will absorb into the soil surface as infiltration when it rains. The Benanain watershed is dominated by soil types with scaly clay lithology containing other rock blocks with low to very low permeability and grouped into HSG-D groups with an area percentage of 25.667%.
The curve number value of the Benanain watershed ranges from 56.55 to 73.90, where the highest curve number value is found in the W-310 sub-basin which is dominated by the type of scaly clay containing boulders of other rock. The land cover in the form of shrub agriculture with an area of 22.61 km 2 or 0.21%. The runoff depth value increased by 8.68% with increasing rainfall depth, and the increased runoff depth is directly proportional to the increased curve number value of 3.14%. Determination of CN value with a large watershed area and the high variability of rainfall intensity has a significant effect on the CN value in Benanain watershed. For further analysis with flood hydrograph using the HSS SCS method, it is necessary to have long rainfall data and observations runoff depth are required as calibration data for controlling the use of curve numbers.

Data Availability Statement
The data presented in this study are available on request from the corresponding author.

Funding
The authors received financial support from Institute for Research and Community Services (LP2M) at Nusa Cendana University for the research, authorship, and/or publication of this article.