ESTIMATION OF NRCS CURVE NUMBER FROM WATERSHED MORPHOMETRIC PARAMETERS: A CASE STUDY OF YIBA WATERSHED IN SAUDI ARABIA

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 7, Issue 2, March-April 2016, pp. 247–265, Article ID: IJCIET_07_02_022
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ESTIMATION OF NRCS CURVE NUMBER
FROM WATERSHED MORPHOMETRIC
PARAMETERS: A CASE STUDY OF YIBA
WATERSHED IN SAUDI ARABIA
Mohammad O. Alagha, Saud A. Gutub
Faculty of Civil Engineering,
King Abdulaziz University, Jeddah, Saudi Arabia
Amro M. Elfeki
Faculty of Meteorology,
Environment and Arid Land Agriculture,
King Abdulaziz University Jeddah, Saudi Arabia
ABSTRACT
The NRCS-CN equation for flood predictions relies on the value of the
Curve Number and the amount of rainfall event to determine the
corresponding runoff. Usually, the curve number value (CN value) is extracted
from the tables that follow United State land features classification which
might not be applicable to the land features in Saudi Arabia. This research
paper doesn’t use NRCS-CN table values form of the US for estimating the
curve number value, rather, the CN values have been estimated from the data
of rainfall and runoff events of some gauged watersheds in the western region
of Saudi Arabia (Yiba watershed and its sub-basins). The observed CN values
are in the range of 61 and 99. For the 1984-1987 rainfall events, the CN
behavior follows the standard regime with an approached value, of 52.
It has also been shown that there is a relatively good agreement between the
observed CN and the theoretical NRCS-CN curves with the factor of initial
abstraction (λ = 0.2). The watershed morphometric characteristics have an
effect on the value of the curve number. Some parameters give a strong
relation with the average CN such as basin average elevation, shape factor,
basin slope, basin Length, and watershed area where R2
(i.e., R-Square which
known as the coefficient of determination) is 0.99, 0.81, 0.87, 0.78 and 0.56
respectively within some range of the specified parameter given in each
equation. These relationships could be used to estimate average curve
numbers for similar basins without relying on NRCS-CN tables.

Mohammad O. Alagha Saud A. Gutub and Amro M. Elfeki
Keywords: Curve number, runoff calculation, Saudi Arabia, Yiba watershed,
floods, NRCS method, and regression analysis.
Cite this Article: Mohammad O. Alagha, Saud A. Gutub and Amro M.
Elfeki, Estimation of NRCS curve number from watershed morphometric
parameters: A Case Study of Yiba Watershed in Saudi Arabia, International
Journal of Civil Engineering and Technology, 7(2), 2016, pp. 247–265.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=7&IType=2
1. INTRODUCTION
The estimation of the expected runoff resulting from rainfall is very important for
flood mitigation studies. The direct runoff estimation can not only be used for flood
analysis but it is also useful for agricultural irrigation, electricity generation in many
countries. Many methods are used to predict runoff. One of these methods which, is
widely used, is the Soil Conservation Service Curve Number (SCS-CN) method and
its name was changed in 1994 to Natural Resources Conservation Service (NRCS)
method (Ferguson, 1988). The NRCS-CN method estimates runoff depth by the
following equation,
(1a)
(1b)
where P is the rainfall depth (mm), Q is the Runoff depth (mm), and S is the
potential maximum storage which is given by,
(2)
where CN is the curve number parameter. Its value is extracted from the tables
formulated by the United States Department of Agriculture (see e.g. Technical
Release 55, 1986). The CN ranges from 30 to 100; the minimum values indicate low
runoff, however, the values of curve number close to 100 express high runoff. The
curve number is dependent on multi factors, for example, land use, soil type, and
moisture condition.
This method has been established by the United States Department of Agriculture
and it depends on the type of land use and land cover of agricultural watersheds in the
United States which could be different from the type of land use and land cover
characteristics in Kingdom of Saudi Arabia (KSA). The land cover in Saudi Arabia is
mainly mountainous with ephemeral streams, sand dunes, fine bed sediments in the
stream networks, and has sparse vegetation in the stream course.
There is a discussion in the scientific community of water resources concerned
with a capability of using the NRCS-CN method in hilly watersheds because the
method is developed for flat farmland, so it doesn't take into account hilly features
such as in KSA.
The major factors affecting runoff generation are: soil type, land use, surface
condition, antecedent moisture condition, and treatment. These factors are
incorporated in a single CN parameter. The NRCS-CN shortcomings are the
following: (1) it does not take into account the effect of spatial scale, (2) it does not
take into account the effect of rainfall intensity and its temporal distribution, (3) it is
deeply sensitive when incorporating multi factors (e.g. soil type, land use, surface
condition, antecedent moisture condition and treatment) in a single parameter; and
(4) it does not take the effect of the adjacent moisture condition into consideration

Estimation of NRCS curve number from watershed morphometric parameters: A Case
Study of Yiba Watershed in Saudi Arabia
(Hawkins, 1993; Ponce and Hawkins, 1996; Michel et al., 2005). The Common
technique of estimation of NRCS-CN is as follows (Naseela, et al., 2015):
1. Select and map the outlines of the drainage basin for which curve number needs to be
calculated.
2. Determine the area of the drainage basin.
3. Map the soil types and land use for the drainage basin of interest.
4. Convert the soil types to hydrologic soil groups.
5. Overlay the land use and hydrologic soil group maps, identify each unique land use
soil group polygon and select the area of each polygon.
6. Assign a CN to each singular polygon, based on standard NRCS-CN table.
7. Calculate an overall CN for the drainage basin by area-weighting the land use soil
group polygons within the drainage basin outlines.
Ebrahimian et al. (2012) studied the estimation of runoff using standard and slope-
adjusted NRCS-CN method in the Kardeh watershed, northeastern Iran. The effects
of slope on CN values and runoff depth were determined using a slope-adjusted CN
equation. The correlation between estimated and observed runoff depths has r = 0.56,
at a rainfall depth P < 0.01. The results showed that the slope-adjusted CN equation
appeared to be inappropriate for runoff estimation in steep slope watersheds, the
standard CN method can be used with 55% accuracy in such watersheds for
watershed management but not for flood estimation.
Shrestha, et al. (2013) investigated the effect of slope on curve number through
experimental plots that contain maize crop. They used measured rainfall and runoff
data. The investigated watershed slopes in their study are 1%, 3%, and 5%. Applying
the infiltration test using double ring infiltrometer to the soil resulted in a soil type of
the type of a Hydrologic Soil Group C. These soils have a low rate of water
transmission (1.27-3.81 mm/hr). The results showed positive correlations between CN
and slope.
Tedela N. et al. (2012) studied the accuracy and consistency of the NRCS-CN
method using rainfall-runoff series from 10 small forested-mountainous watersheds in
the eastern United States, they used eight annual maximum series, and these series are
the basis to compare tabulated curve numbers with values estimated using five
methods. The results show that the Runoff estimates using tabulated CN are
unreliable to estimate runoff for 9 of the 10 forested mountainous watersheds. CN
chosen for the forests of the Appalachian Highlands requires independent calibration
to watersheds delegate of the regional landscape.
In this research paper, the authors have not used NRCS-CN tables to estimate
runoff based on the aforementioned method; however, the CN values are obtained
from rainfall and runoff data of a gauged watershed in the western region of Saudi
Arabia. In the current study, an attempt is made to relate the parameter to the
morphology of the basin. To the best of the authors’ knowledge, this is the first
attempt to investigate such a relation. Therefore, a black box approach is followed
using regression analysis between the observed CN from rainfall-runoff events and
watershed morphometric parameters. The values of CN obtained from such study
reflect the common values that are expected to be prevailing in the Kingdom of Saudi
Arabia (KSA), especially for the south western part of KSA. Yiba watershed is
utilized for such study. A complete description of such an area is given in the next
section. The proposed approach helps researchers and engineers to obtain CN values
from morphometric parameters rather than the classical method of estimation of CN

from Tables of NRCS-CN. The morphometric characteristics that have been used in
the study are focused on five parameters: the watershed area, the basin length, the
basin slope, the shape factor and the drainage density. Figure 1 shows a sketch for
these parameters.
Figure1 Morphometric parameters used in the current study
2. THE STUDY AREA
The study area is located in the south western part of Saudi Arabia. Figure 2 a, shows
the location of the study area. It is in Asier district which is about 380 km away from
Jeddah city, lying between 41°15′ & 42°10′ longitudes and 18°50′ & 19°35′ latitudes
with an area of 2830 km2
. In this area, there is an experimental watershed called Yiba
watersheds, of whose rainfall and runoff depths were measured during the period of
1984 up to 1987 (Dames and Moore, 1984).
3. DATA COLLECTION
The data in this study consists of rainfall and runoff measurements. The number of
rainfall events used for this study is around 82 events in the period (1984 -1987).
Figure 3 shows a sample of rainfall-runoff event at station SA401 which has
happened on 14 May 1985. The location of the runoff station is shown in Figure 4.

Figure 1 a) Location of Yiba watershed, western region of Saudi Arabia b) Digital elevation
model (Modified from Elbishi, 2015).

b)
Clock Time(hr) Rainfall (mm)
15 0.6
16 4.8
17 6.4
18 2.5
19 0.6
20 0
21 0.0
22 0
23 1.1
c)
Time (hr) Q (m3/s)
17.4 0.00
17.6 19.47
17.9 41.15
18.4 32.70
18.8 23.85
19.9 3.14
20.8 2.84
21.7 2.48
23.6 0.81
23.7 0.73
23.8 0.65
23.9 0.57
24.0 0.49
24.1 0.41
24.2 0.33
24.3 0.24
24.4 0.16
24.5 0.08
24.6 0.00
(a)
Figure 2 a) Sample of rainfall - runoff event (14 May 1985) at station SA422. b) Table of
recorded rainfall data, c) Table of recorded runoff data (Dames and Moore, 1984).
a)

4. METHODOLOGY
The NRCS-CN general equation (Chen, 1982) is given by:
(3)
where P is the rainfall depth (mm), Q is the Runoff depth (mm), λ is the
coefficient for initial abstraction, Ia and S is the potential maximum storage.
In the current study, the estimation of CN is made through the application of the
following equations for rainfall and runoff events in the study area. Taking into
account λ = 0.2, Equation (3) reads,
(4)
and CN is estimated from S as,
(5)
Figure 3 Yiba watershed, their sub-basins and runoff stations (Modified
from Elbishi, 2015).

The S value is obtained by substituting rainfall and runoff depths in Equation (4)
and the value of the curve number is obtained by substituting S in Equation (5). The
next flowchart explains the methodology used in the current study.
4.1 Estimation of CN values from rainfall-runoff data
The CN values have been calculated using Equation (4) to obtain S, which expresses
the maximum potential storage, then substituting S in Equation (5) to get the CN
value, Table 1 shows the estimated CN values from rainfall-runoff events in the study
area in the period 1984-1987. Average rainfall values of curve number are obtained
for each sub-basin and regression analysis is applied on these average values since
these values heavily depend on rainfall data. Table 2 shows the average values of CN
and some statistical measures of CN. The upper and lower limits of 68% confidence
of the average CN values are represented in Figure 6. The results show considerable
variation in CN for stations SA401 and SA422. However, the variation is relatively
less for stations SA423 and SA424.
Table 1Estimated CN values from rainfall-runoff events.
CNEvent DateCNEvent DateCNEvent DateCN
Event
Date
Station
9115-Aug-858412-May-857423-Apr-858114-May-84
SA401
6801-Mar-878320-May-858728-Apr-859121-May-84
8822-May-858801-May-858220-Sep-84
8211-Jun-857905-May-856205-Apr-85
8417-May-857105-May-857223-Apr-858820-Sep-84
SA422
7222-May-858412-May-858901-May-856705-Apr-85
93
89
90
80
75
15-Apr-86
16-Apr-86
22-Apr-86
07-Jun-86
01-Mar-87
89
94
97
92
28-Apr-85
11-Jun-85
04-Sep-85
21-Sep-85
94
76
91
86
17-Nov-84
05-Apr-85
11-Apr-85
22-Apr-85
81
89
88
90
12-May-84
13-May-84
21-May-84
19-Aug-84
SA423
88
94
92
77
02-Mar-86
16-Apr-86
07-Jun-86
01-Mar-87
94
95
90
96
11-Apr-85
15-Aug-85
16-Aug-85
04-Sep-85
93
94
93
64
19-Aug-84
19-Sep-84
20-Sep-84
05-Apr-85
92
89
86
91
12-May-84
13-May-84
14-May-84
21-May-84
SA424

Figure 4 Flow-chart illustrates the application of the proposed methodology.

Table 2 Some statistical measures of curve number calculated from rainfall and runoff data.
Station
Number of
rainfall (event)
Average Curve
Number ( )
Standard
deviation, σ, of
(CN)
Upper and
lower limit for
68% confident
+σ -σ
Station SA 401 20 86 10 96 76
Station SA 422 14 84 12 96 72
Station SA 423 26 90 9 99 81
Station SA 424 22 91 8 99 83
Figure 5 The average CN values and its upper and lower limits with 68% confidence.
4.2 Extraction of Yiba watershed and its sub-basins.
Firstly, to start the delineation process for a specific watershed, it is required to know
the location of the basins’ outlet and the digital elevation model (DEM) of the study
area. The available DEM has multiple resolutions such as 30 m and 90 m. The
available DEM used for this study is 90 m, which was obtained from King Abdelaziz
City for Science and Technology (KACST). The delineation process has been done by
Watershed modeling system (WMS7.1). Figure 6 shows Yiba watershed and its sub-
basins at the runoff station indicated in the figure.
4.3 Estimation of morphometric parameters of the basins.
The morphometric parameters considered in this research are explained in Table 3.
These parameters are: the area of the basin, the shape factor, the basin average
elevation, the basin slope and the length of the basin.
86
84
90
91
76
72
81
83
96 96
99 99
70
74
78
82
86
90
94
98
SA401 SA422 SA423 SA424
CurveNumber
Yiba Watershed sub-basin at the specified satations

Table 3 Morphometric parameters considered in the study.
DefinitionSymbol
Morphometric
parameter
The area of the basinA
Area
Basin shape factor (SF)
Where, Lc = The distance along the main channel from the basin
outlet to the point on the main channel opposite the center of
area (centroid). Lw= The length of the watershed. (α = 0.3 for
length measurements in kilometer)
SFShape Factor
The slope of the basinBS
Max stream
Slope
The Basin Average Elevation of the watershed, calculated from
the digital elevation model (DEM).
BAE
Basin Average
Elevation
The distance between the outlet and the most distance vertex on
the boundary of the basin.
BLBasin Length
The estimated values of these parameters are extracted from WMS software and
are summarized in Table 4. These values are later plotted against the estimated
values for further analysis as given in the next section.
Table 4 Morphometric parameters for all sub-basins of Yiba watershed.
Stations
Area (km2
) Basin
Slope
Shape
Factor
Basin
average
elevation(m)
Basin
Length
(km)
SA401
785
0.28 1.61 1056 35
SA422 322 0.33 1.67 1201 23
SA423 597 0.27 2.08 880 36
SA424 2305 0.20 2.02 771 52
4.4. Regression analysis
A regression analysis approach is followed to find out relationships between and
morphometric parameters given in the previous section. The analysis is based on the
least square method and a fitting equation is obtained for each parameter. The
criterion of the best fit is made through the evaluation of coefficient of determination,
R2
(Andale, 2016).
5. DISCUSSIONS OF THE RESULTS
5.1 Relationship between CN and Rainfall Depth
Hawkins (1993), classified rainfall- runoff system behavior into three categories.
These categories are complacent, standard and violent variations. In the complacent
behavior, the CN declines steadily with increasing rainfall depth. In the standard
behavior, the CN declines with increasing storm size as in the complacent situation,
however in the standard behavior, the CN approaches a near-constant value with
increasingly large storms. The violent behavior has a different pattern where CN rises
suddenly and asymptotically approaches an apparent constant value. Complacent
behavior often appears at lower rainfall. The CN is plotted against the rainfall depth

as shown in Figure 7. The observed CN declines with increasing storm rainfall depth.
The equation of the standard behavior is in the form of Equation (6) Hawkins (1993),
(6)
where is a constant approached as ; and b is a fitted constant.
The least square method is used to estimate the fitting parameters. The final form
of the equation is given as,
(7)
It has been observed that the CN are highly dependent on the value of the rainfall
as confirmed by others researches such as Hawkins (1993) and Kazimierz (2010).
The equation that describes the complacent behavior is given by,
(8)
The equation gives the threshold of runoff at rainfall depth, or where P = 0.2S, the
CN value from complacent behavior cannot be used safely for design purposes
because no constant value has been clearly approached.
Figure 6 CN behavior with the size of the storm
5.2 Comparison between theoretical CN and observed CN.
In Figure 8, the observed runoff depths are plotted against the total rainfall depths.
Each data point represents one storm and it is depicted with different symbols
depending on the range of CN values according to the upper and lower limits as given
in the table below, Runoff predictions of the NRCS-CN method for the CN values are
estimated using Equations (1a) and (2). The observed CN has been plotted on CN
theoretical curves

Table 5 Limits of categorization of the CN values: A: is the lower limit and B: is the upper
limit for each category
CN Theory
Mean Values
Limits of CN values for storm categorization of storm data
A ≤ CN < B
65 60 ≤ CN < 70
75 70 ≤ CN < 80
85 80 ≤ CN < 90
95 90 ≤ CN < 100
(USDA, 1986). The initial abstraction (Ia) used has the standard value of 0.2. It is
obvious, that there is an agreement between the observed CN and the theoretical CN
curves.
Figure 7 Rainfall-Runoff scatters diagram showing the comparison between theoretical CN
mean value, upper-lower limits, and Observed CN.
5.3 Relationship between and Basin Average Elevation (BAE).
Figure 9 graph (a) shows a relationship between average CN for the storms at the
watershed and BAE in meters. An equation in form of
; 770 ≤ BAE ≤ 1200 m (9)
is fitted to the data under the condition given in the equation. The R2
for the fit is
0.99 which shows a very good relationship.
5.4 Relationship between and Basin Shape Factor (SF).
Figure 9 graph (b) displays a relationship between average CN and SF. An equation in
the form of

; 1.60 ≤ SF ≤ 2.00 (10)
for the fit is
0.81 which shows a relatively very good relationship.
5.5 Relationship between and Basin Slope (BS)
Figure 9 graph (c) shows a relationship between average CN and BS. An equation in
the form of
; 0.20 ≤ BS ≤ 0.30 (11)
is fitted under the condition given in the equation. The R2
for the fit is 0.87 which
shows a relatively very good relationship.
5.6 Relationship between and Basin Length (BL)
Figure 9 graph (d) shows a relationship between CN and BL in kilometers. An
equation in the form of
; 20 ≤ BL ≤ 50 km (12)
for the fit is
0.78 which shows a good relationship.
5.7 Relationship between and Watershed Area
Figure 9 graph (e) shows a relationship between CN and Area in square kilometers.
An equation in form of
; 320 ≤ Area ≤ 2300 (km2
) (13)
for this fit is
0.56 which shows a reltively moderate relationship.

Figure 8 Relationship between and watershed parameters.
Table 6 summarizes the empirical equations derived in the current study and the
range of CN obtained under the limits of applicability of these equations. The
equations produce almost the same order of magnitude of upper and lower limits. The
average lower limit of is 85.2 and the upper limit is 91.2. The coefficient of
variation, CV, for both minimum and maximum values is very small (CV<<1). These
results lead to a conclusion that any of these equations can be used for the estimation
of with relatively very small error.

Table 6 Comparison of the upper and lower limits of the CN from various equations
Parameters Equation Validity of the equation Min CN Max CN R2
Basin
average
elevation
= 105-0.017 BAE 770 ≤ BAE ≤ 1200 (m) 85 92 0.99
Shape
factor
= 65+12.2 SF 1.65 ≤ SF ≤ 2 .00 85 89 0.81
Basin slope = 103 - 55.1 BS 0.20 ≤ BS ≤ 0.30 86 92 0.87
Basin
length
= 79 + 0.243 BL 20 ≤ BL ≤50 km 84 91 7.08
Area = 85+0.003 Area 320 ≤ Area≤ 2300 km2
86 92 7.06
Average =
Standard deviation =
Coefficient of variation =
85
0.84
0.01
91
1.3
0.014
6. VALIDATION
The validation process has been performed for the runoff volume and peak discharges
by comparing both the observed runoff volumes and peak discharges with the
computed runoff volume and peak discharges. The validation is based on the
developed formulas of CN in the current study. Equation (9) is adopted for the
validation process since it gives the highest R2
of 0.99.
6.1. Validation by Runoff Volume
Figure 10 shows a scatter plot between the observed and estimated runoff volumes. A
45 degrees line is added to the figure to test the model performance. The obvious
inspection of the results shows relatively reasonable agreement.

Figure 9 Scatter plot between the observed and the computed runoff volumes.
6.2 The Peak Runoff Discharge Validation
The peak discharge validation has been performed through the NRCS for TR-55
(USDA, 1986) model given by the formulae,
(14)
where Qpeak is the peak discharge (m3
/s), A is the area (km2
), and Q is the depth of
runoff (mm). Q is calculated from the curve number NRCS equation and the CN
value has been obtained from Equation (9), and qu is the unit peak discharge
(m3
/s/km2
/mm), which is calculated from,
qu = (15)
where, is the conversion parameter (0.000431 in metric units), tc is the time of
concentration, and C0, C1 and C2 are constants based on the storm type (Type II).
The time of concentration, tc, has been calculated by the equation,
(16-a)
(16-b)
where, is the lag time (hr), L is the watershed length (m), CN is the curve
number, and H is the average watershed land slope (%).
The values of C0, C1 and C2 are constant factors which have been obtained from
Table (7).
In Figure 11, the observed Qpeak are plotted against the computed Qpeak, with an
additional virtual line of 45 degrees. It should be mentioned that a correction factor of
4.5 has been used to get a reasonable agreement between the observed Qpeak and the
computed Qpeak. The justification of this correction factor has two sides: first is that
the storm pattern in Saudi Arabia does not match the NRCS-Type II storms (Elfeki, et
al., 2013), and second is that the NRCS equation for peak discharge is derived in

temperate areas that have different characteristics distinct from Saudi Arabia (Elbishi,
et al., 2016).
Table 7 The values of C0, C1 and C2 for Type II storms (Source: TR-55, USDA)
Rainfall Type Ia/P C0 C1 C2
Type (II)
0.10 2.55323 -0.61512 -0.16403
0.30 2.46532 -0.62257 -0.07020
0.35 2.41896 -0.61594 -0.08820
0.40 2.36409 -0.59857 -0.05621
0.45 2.29238 -0.57005 -0.02281
0.50 2.20282 -0.51599 -0.01259
Figure 10 Scatter plot between the observed runoff and computed peak discharge.
7. CONCLUSIONS
The results show that the curve number, CN, depends on the rainfall event. For Yiba
watershed and under the rainfall events during 1984-1987, the CN behavior follows
the standard regime with an approached value of 52. It has also been shown that there
is a relatively good agreement between the observed CN and the theoretical NRCS-
CN curves with the factor of initial abstraction (λ = 0.2). The watershed parameters
have an effect on the value of the curve number. Some parameters give a strong
relation with the average CN such as the basin average elevation, shape factor, basin
slope, basin Length, and watershed area where R2
is 0.99, 0.81, 0.87, 0.78 and 0.56
respectively within some range of the specified parameter given in each equation

(Table 6 summarizes the results). Through the validation process, it has been shown
that the empirical equation that relates CN to the basin average elevations is relatively
good in representing the volume. However, the validation for the peak runoff required
some correction factor of 4.5 to get a reasonable fit. The reason for that has two folds:
first is that the storm pattern in Saudi Arabia does not match the NRCS-Type II
storms and second is that the NRCS equation for peak discharge is derived in
temperate areas that have different characteristics that is different distinct from Saudi
Arabia.
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maturity?, J. Hydrol. E.-ASCE, Vol.1, No.1, pp. 11–18.
[13] Michel, C., Andréassian, V. and Perrin, C. (2005) Soil Conservation Service
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ESTIMATION OF NRCS CURVE NUMBER FROM WATERSHED MORPHOMETRIC PARAMETERS: A CASE STUDY OF YIBA WATERSHED IN SAUDI ARABIA

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ESTIMATION OF NRCS CURVE NUMBER FROM WATERSHED MORPHOMETRIC PARAMETERS: A CASE STUDY OF YIBA WATERSHED IN SAUDI ARABIA