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DOI:10.22059/jwim.2022.337092.959
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Evaluation of Rainfall-Runoff-Retention Model (3RM) in Kassilian and Darjazin Watersheds
Saeedeh Izadi1, Shayan Shamohammadi2*
1. M.Sc. Graduated, Department of Water Engineering, Faculty of Agriculture, University of Shahrekord, Shahrekord, Iran.
2. Professor, Department of Water Engineering, Faculty of Agriculture, University of Shahrekord, Shahrekord, Iran.
Received: April 17, 2022 Accepted: January 10, 2022
Abstract
Hydrological models make it possible to simulate the rainfall-runoff process, the amount of runoff from rainfall in areas without statistics or with incomplete statistics. One of the most practical and globally accepted rainfall- runoff model provided by American Soil Conversation Service, (SCS) known as SCS-CN where CN refer to Curve Numbers based on soil hydrological conditions. In this research, Rainfall-Runoff-Retention Model (3RM) was used introduced the new concept for rainfall Interceptions as Antecedent Effective Retention (IER) instead of the Antecedent Moisture Content (AMC) and calculating it by water balance method. SCS-CN model with this new revision were applied in Darjazin (semi-arid climate) and Kassilian (very humid climate) catchments in Iran. The results of the study showed that Darjazin watershed with 29.38 persent rock cover (D) and 3.27 persent hydrologic soil group (A) with a holding potential of 20.66 mm and Kassilian watershed with forest cover 77 persent and rock mass cover 0.0 persent has a lot of retention potential (51.11 mm). The value of α (ratio of initial retention to potential retention) was obtained between 0.05 and 0.13 in different basins. Also, the results of model fitting on rainfall-runoff data showed that the evaluation indices including coefficient of determination R2, RMSE, NRMSE and NSE for predicting runoff in Darjazin catchment (0.998, 0.439, 0.029, and 0.998) respectively, while the same indicators for the Kassilian watershed are (0.867, 0.264, 1.009 and 0.859) respectively. The results show that the model has an acceptable ability to predict runoff and actual retention in all two watersheds.
Keywords: Previous effective retention, Water Balance, Watershed, 3RM.
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Table 1. General characteristics of Kassilian and Darjazin watersheds
Average Annual Rainfall (mm) Geographic Area
Slope (%) Average height
(m) Area
(Km2) Name of
the watershed Eastern Length Northern Latitude
813.80 35° 58´ 30´´ - 36° 7´ 15´´
53˚ 8ʹ 44´´- 53˚ 15 ʹ 42´´
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Figure 6. Steps of studying and evaluating 3RM in order to estimate runoff of Kasilian and Darjazin catchments.
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X
> p B .4 01
" ) Z
2>
4
? 1 " ) 2
D
) >) 1
2 I# R( I .( 1 = (
( # K
&4# > + . ( 4 5=
1 >
I# h# &u:# R 7 4
" ) j (
R 7 4 + \ &
e I# h# u:#
\ 9 ? \ 1
(?
4 5= ( 4 5= 4 .
) + I7
" ) (α
2> ? 1 05
/ 0
13 / 0 +, )
>) 4 ( " ( .(
, $
CN -
1 SCS
2 / 0 )
Ponce
Hawkins, 1996
&
01 ( / + .4#
4 > 4 5= # K K 8 A . 1 >
9 : 4 5= ( EF
4 5= ! ,
8c 9 ) 4# 2!
5 6 Y * a G " (
+ I7 4 5= 4 ( 4 5= 05#
4 &4# 1 7 R 2!
4#
$ /
SCS-CN
0
$ &$ . X
D 7 8 , 2! ; $ 0 (I
8 , $ " # , & 67
$ 1 4#
SCS-CN
$ 4 G o "
0 ( h# I CDX & I# # D 7 )
Mockus, 1949
(&
g X p B 1
p # g g I CN
+ I7 4 5= p #
.
Shamohammadi (2013)
Z B 01 α
"
10 , 2 @ / " ) 4#
1 /
L I " ;3IX R w7
&
/ 4?\
* 1 j ! ,
) 4 5=
Ia
( # b \
4 5=
EF D 7 4 >
4 ) . 1 >
( e ?1
Ia
( "
01 I
/ 4#
)
Shamohammadi, 2017
( 4 5= ~1 ) .
) + I7
Smax
" ) ( 2> ? 1
Z
11 / 51 76 / 24
* &
( : 1
4 5=
Smax
+, )
: 9 : " )
? 1 " ) :4# . + ( . 2> " ) <
( 4 5= s I 7 Y * 2 ] A &4# 6* E + I7 4 5= +1 4 5=
R Ek (e\
4 5=
St
Smax
.
? 1 " ) 2
/ 77 B 1 " ) u:# ,
?= >
r _IX X
>) 4#
3 &(
, h(! 1 2 / 8 . = # R 7 B " ,
>
e = # R 7 1 " 05#
2> " ) = # R 7 & I +1 4 5=
87 / 47 2 @ / " ) " , 4# r _IX X
)
Ebrahimian et al., 2012
\ \ eg .(
Z> +
R ? 1 " ) +1 4 5= (
I 7 ( . + I7 4 5=
Fmax
Sp
9 : " +, )
Shamohammadi (2013)
&
2 / 54
2 / 59
? B ) 9 : ( " 1 4# I
R 4 ) .
o E 3\ 1 #
4# 1 & I#" X (:
e5 + \ "
.4# + I7 4 5= ~1 ) 4 5= R 2!
Table 2. Soil hydrological group coverage (%) Darjazin Kassilian
Hydrological group
3.27 24.60
A
32.96 69.10
B
34.39 6.30
C
29.38 0.00
D
Table 3. Catchments land use coverage (%)
Land use % Rocky Pasture Forest Cultivate Residential and Rivers Rainfed Wasteland
Kassilian 8.20 7.30 77.2 6.10 1.20 0.00 0.00 Darjazin 47.87 45.23 0.00 4.45 2.45 0.00 0.00
Table 4. Results of 3RM fitting on Rainfall-Runoff data of Kassilian and Darjazin Watershed
Rainfall-Runoff model and important parameters Watershed
Q Pa 51.11 Pa 48.56 Pa"
I 2.55mm
.
α c7 =0.05
Kasilian
Q Pa 24.76Pa 21.52 Pa"
I 3.24mm
.
α c7 =0.13
Darjazin
) + 7 9 : $" (
D +1 4 5=
e . o)3 1 *
+1 4 5= Z &$ ( R 2! &
+c )
+ D0"
R 1 " ) ( &
G 1
C \ " 4 5= Z ' g " d/
L
p R 1 1
"
1
Pa
4e#
4 5 . 1 +
A, \ 2 4 5= Z 8 ,
C 2 # X ~1 ) 4 5= ( )
4 E &
: ) 13 ((
.
$ K (
- ) + ' 8
1 ) (
? 1 2 @ / " ) ' Z 1 4# / "
01
" ) "
2>
/ + 1 &
?= > aG 67] A 2 R 2! s
8 , .4
? 1 2 @ / " ) 1
" R r _IX 77
Z> & ?= > R 7 ,
01 4 ' ( R 2! 4\ #
" ) 1 4# ) &4# 2>
" ) ' Z & * R 2!
. 1 X + C \ 4e#
Figure 7. 3RM output (in Excel environment) in estimating the actual retention of Kassilian and Darjazin catchments.
Figure 8. Runoff relationship of Kassilian and Darjazin catchments (3RM output in Excel environment).
St=Pa= I
0 5 10
0 5 10 15
St (mm)
Pa(mm) Dar
St(Model) St(Cal.) Bisector line St=Pa=I
0 5 10 15 20
0 5 10 15 20 25 30
St (mm)
Pa(mm) Kas
St(Cal.) St(Model)
Linear (Bisector line)
0 3 6 9
0 2 4 6 8 10 12 14 16 18
Q(mm)
Pa (mm) Kasilian Darjazin
) + 9 0 8 q ( 8 q +1 4 5= "
" ) ' 9 :
D .
4\ # R 1 4 5= 8 q Z R 1 " ) R 2! ' 8 q Z &i X +X '/ ] A
R 4\ # ' > I!
R 2!
.
0 & Y *
Z 8 q 1 1 s I#
Z 8 q ;3X +1 4 5=
&4# '
* Z ' Z p eg e 1
C \ 4 5=
9 ) 9 p B .(
05 " ) 1 4# & 1 1 4 5= Z & * R 2! ? 1 2 @ /
R 4\ # R 2! 2> " ) 4
' Z 2 + ( 4\ #
R 4 )
R 1 ( 2> " ) .
4) + \ * * R 7 & " )
? . L I 8 E Z> 1 4 ?, R w7 .4#
) + 10 ) ( 4 5= 8 q ( &(I
9. ~1 ) 4 5=
)
Fmax
4 5= 8 q (
) + I7
Smax
/ ( e (
" )
9 : D e &
o)3 1 *
I 7 # 8 q =
4# ‚ e
( 01 " ) 9. 4 5=
"
(
p B .4# + I7 4 5=
4 e 45> "
) # C 1 13
( I)
(
Fmax
&
Smax
) & 1 # K I
# K 1
$ 05 I 7 " C & ƒ 7 &SCS
"
7 .4# 2
Figure 9. Real retention changes with runoff in Kassilian and Darjazin catchments.
Figure 10. Demonstration of I, Fmax and Smax with potential retention in Kassilian and Darjazin.
0 2 4 6 8 10 12
0 5 10 15
Q&St (mm)
Pa (mm) Dar
Q(Model) St(Model) 0
2 4 6 8 10 12 14
0 5 10 15 20 25 30
Q&St (mm)
Pa (mm)
Kas Q(Model)
St(Model)
0 5 10 15 20 25 30 35 40 45 50 55 Smax
Fmax I
Smax, Fmax& I (mm) Kas
0 5 10 15 20 25
Smax Fmax I
Smax, Fmax& I (mm) Dar
" L I 7
4K, g #
) >
5 ( 4# D + . 9 Z B .
Z
" ) R 7 2> ? 1
'
859 / 0 &
998 / 0 + I7 4 5=
934 / 0
999 / 0 ( 1 +, ) 4#
K /
+ . . # I! * . p B .4# ^.
-X K "
<1.009 RMSE
0.439<
&
NRMSE<0.264
<
0.029
<0.998
0.867<NSE
&
k . / . *
RMSE
NRMSE
\ C 2 A, . Y 4 ~
D .4# +
R2
2
\
0
1 C 2 C \ 1 2 1 4# +
&
(? eI\ + . .
=0 R2
b \ 9 2
0 =I ) 4#
Moriasi et al., 2007
.(
9 (
NSE
1 −∞
+ .
NSE=1
I + 1 | : 1 4# I )
NSE=0
R 7 4. 1 = "
01 " 4#
) A, "
NSE<0
1 ) (
R 7 1 4# / "
= D
R 7 " I5 ) 4#
1970 Nash &
Sutcliffe,
(…
-X K >
) >
5 f &(
R 7 4 ? . ( *
" ) 4 5= '
? 1 2>
.4# I 8 AI * R 7 0 ?.
Table 5. Values of statistical indicators for estimating Runoff (Based on validation data)
Q Smax
Index Watershed
0.859 0.934
R2
Kasilian RMSE 1.008 1.009
0.264 0.131
NRMSE
0.867 0.930
NSE
0.998 0.999
R2
Darjazin RMSE 0.439 0.439
0.029 0.029
NRMSE
0.998 0.998
NSE
4 3&
5
f " AI#
R w7
$ - 4 E '
" )
? 1 2 @ /
) + I7 4 5= & 2>
Smax
( Z 11 / 51
76 / 24
? 0 . +, ) I
4 5= 4 Y
) + I7 4 5= (
2 (α
Z 05 / 0
13 / 0 # K I .
1 = 05 g
* # "
9 : ( 4 5= ( 9 & +, )
) " 1 2> ? 1 2 @ / " ) (I
( +B A
Fmax
Smax
Z 55 / 2 24 / 3
? I 4#
. / 0 ?. ? 1 2 @ / " )
9. 4 5= ( & ?= > R 7 ' G R ) 56 / 48
? I CDX " ) 4 (
) 2>
52 / 21
? D 9 : L I . ( I
/ 3 $ 1 o
4 5= /
EF ) D 7
IER
* " +, ) ( L 7
&+ . "
. / 1 $" L I
$ -
' " AI#
-X
"
Z B +
& 9 D
8 9 :X
= &
D
=
8 9 :X R 7 R Z B
? 1 2> " ) ' Z
) 998 / 0 &
439 / 0 &
09 / 18 998 / 0 ) ( 866 / 0 &
905 / 0 &
255 / 0
889 / 0 +, ) ( Z 1 L I > .
&
4A*
R 7 3RM
4 5= '
" " ) 9.
+ . . X
.4#
L I B ) 9 : 1 D
#
2 @ / " ) $ + (I E 4# 7 C ( # K
&I F St
8 , o
. * 1 #
AI#
=I " I) #
R "/ " 4# 4! + . I
i X ^ # " ) u:# R 7 9 : #
I)
"
" ) Z ] A * .
B )
" I# 7 4 5=
:X
"
+. ) 0 . #
1 4 5= & Y
&4# 05 I 7
"
+ . $ (
# K > D 7 4 5= .
$ G * >
# K
4
$
" 1 SCS
) K e 7
AI# ( I * j3 1 & 1
.4# 8 AI AI#
5 D 7 B ) "
&
$ - '
* K 1 ' @I
5A
d . ‚ e
l :# 4# b"c 8 ,
D 7 ) $
@ / "
'c Y &2 d
9 G "
# ?e>
1 Y C 5 & @I# &
DX C &
2
... ; ' ]
# 0 . * . 5 D 7 Y
R w7
" ) 9
@ / = 2
o 9 "
1 ID 9 :
0 ?. h e I
8 A
# * . .
6 '( &
1. Sone
2. Natural Resources Conservation Service-Curve Number
3. Shamohammadi Constant 4. Regression
5. Root Mean Square Error 6. Normal Root Mean Square Error 7. Nash–Sutcliffe Efficiency
7 8 9 "
€ . > * h# ^! • 9 *
7 8
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