4/
7/
04
1
Implementation
of
a
Probabilistic
Curve
Number
Method
in
the
PRZM
Runoff
Model
James
N.
Carleton
and
Dirk
F.
Young
4/
7/
04
2
Probabilistic
Runoff
Modeling
°
EFED
simulates
runoff
using
Pesticide
Root
Zone
Model
(
PRZM)

°
too
slow
for
Monte
Carlo
4/
7/
04
3
The
Curve
Number
Method
(
)






>

+

 
 
 

=
a
a
a
a
S
I
P
I
P
Q
I
P
for
I
P
for
0
2
Where
Q
=
runoff
(
in)

P
=
precipitation
(
in)

S
=
potential
retention
(
in)

Ia
=
initial
abstraction
(
in)
4/
7/
04
4
Popular
Form
(
)






>

+

 
 

=
0.2S
P
for
8
.

0
2
.

0
0.2S
P
for
0
2
S
P
S
P
Q
10
CN
1000
S
 

=

CN
=
curve
number
[
unitless]
4/
7/
04
5
Antecedent
Runoff
Conditions
CNI
CNII
CNIII
100
100
100
87
95
98
78
90
96
70
85
94
63
80
91
57
75
88
51
70
85
45
65
82
40
60
78
35
55
74
31
50
70
26
45
65
22
40
60
4/
7/
04
6
0
5
10
15
20
25
0
3
6
9
12
S
II
(
inches)

SI
and
SIII
(

inches)
Antecedent
Runoff
Conditions
S
III=
0.427
S
II
S
I=
2.281
S
II
Modified
from
Hawkins
et
al.,
(
1985)
4/
7/
04
7
Curve
Numbers
and
Moisture
From
Kottegoda
et
al.,
1999
(
with
permission)

100
80
60
40
0
100
200
300
400
500
Curve
Number
5
Day
Antecedent
Rainfall
(
mm)
4/
7/
04
8
How
PRZM
Calculates
Curve
Numbers
Soil
Moisture
at
Start
of
Day
0
½
(
FC
+
WP)
FC+
WP
CNI
CNIII
CNII
Curve
Number
FC
4/
7/
04
9
Small
Plot
Data
and
PRZM:
Curve
Numbers
vs.
Soil
Moisture
55
60
65
70
75
80
85
90
0
0.05
0.1
0.15
0.2
Antecedent
Soil
Moisture
(
Vol.
fraction)

Curve
Number
Data
PRZM
relationship
Data
from
Wauchope
et
al.,
1999
4/
7/
04
10
Other
Interpretations
of
ARC
Data
from
Hjelmfelt
(
1991)

0
20
40
60
80
100
0
20
40
60
80
100
Curve
Number
for
50%
and
ARC
II
Curve
Number
for
10%

and
90%

or
for
ARC
I
and
III
90%
10%
4/
7/
04
11
Ia/
SII
as
Lognormal
Distribution
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
Ia/
S
II
Cumulative
Probability
4/
7/
04
12
Implementation
in
PRZM
°
PRZM
code
modified:

 
All
dependence
of
curve
number
on
soil
moisture
removed
 
S
treated
as
constant
at
nominal
value
(
SII)

 
Ia/
S
selected
randomly
from
lognormal
distribution
for
each
day/
iteration
4/
7/
04
13
Implementation,
continued
°
Runoff
calculated
using:

°
`
Equivalent
curve
number'
back­
calculated
for
use
in
modified
PRZM:

(
)






>

+
 
 

=
Ia
P
for
4
Ia
P
for
0
2
Ia
P
Ia
P
Q
]

)

5
4
(

2
[

5
2
/

1
2
PQ
Q
Q
P
S
e
+

 

+

=
4/
7/
04
14
Example
Comparison:
Data
and
Models
0
20
40
60
80
100
0
200
400
600
800
Event
Number
Curve
Number
Probabilistic
Curve
Number
PRZM
Field
Data
4/
7/
04
15
0
20
40
60
80
100
0.09
0.12
0.15
0.18
0.21
0.24
0.27
PRZM­
Calculated
Soil
Moisture
Curve
Number
Probabilistic
Curve
Number
PRZM
Soil
Moisture
Relationship
4/
7/
04
16
Rainfall­
Runoff
Relationship
0.01
0.1
1
10
0.1
1
10
Rainfall
(
inch)

Runoff
(

inch)
measured
PRZM
ARCI
ARCII
ARCIII
4/
7/
04
17
Issues
°
Curve
numbers
and
continuous
simulation
modeling
°
Applicability
to
smaller
rainfall
events
°
Some
sources
of
variability
not
addressed
