online_routing_clark:   Comparison of Clark's unit hydrograph with Ponce's 1989 version 


Formulas

Q = Ij * Ak             Convolution (See text example).

O2 = C0I2 + C1I1 + C2O1        C0 = (Δt/K)/[2+(Δt/K)]

C1 = C0        C2 = [2-(Δt/K)]/[2+(Δt/K)]

References


INPUT DATA:

Unit hydrograph duration tr (hr):     2          Time interval Δt (hr):     1          Storage constant K (hr):     2

Number of increments of [watershed] drainage area:     4

Increments of [watershed] drainage area Ak (km2):     10,30,20,40


SAMPLE OUTPUT:

Time Interval Time (hr) C0I2 (Ponce's Clark)
(km2-cm/hr)
C1I1 (Ponce's Clark)
(km2-cm/hr)
C2O1 (Ponce's Clark)
(km2-cm/hr)
Outflow (Ponce's Clark)
(km2-cm/hr)
C0I2 (Clark's original)
(km2-cm/hr)
C1I1 (Clark's original)
(km2-cm/hr)
C2O1 (Clark's original)
(km2-cm/hr)
Outflow (Clark's original)
(km2-cm/hr)
Outflow (Ponce's Clark)
(m3/s)
Outflow (Clark's original)
(m3/s)
0 0 --- --- --- 0 --- --- --- 0 0 0
1 1 1 0 0 1 1 1 0 2 2.778 5.556
2 2 4 1 0.6 5.6 4 4 1.2 9.2 15.556 25.556
3 3 5 4 3.36 12.36 5 5 5.52 15.52 34.333 43.111
4 4 6 5 7.416 18.416 6 6 9.312 21.312 51.156 59.2
5 5 4 6 11.05 21.05 4 4 12.787 20.787 58.471 57.742
6 6 0 4 12.63 16.63 0 0 12.472 12.472 46.194 34.645
7 7 0 0 9.978 9.978 0 0 7.483 7.483 27.716 20.787
8 8 0 0 5.987 5.987 0 0 4.49 4.49 16.63 12.472
9 9 0 0 3.592 3.592 0 0 2.694 2.694 9.978 7.483
10 10 0 0 2.155 2.155 0 0 1.616 1.616 5.987 4.49
11 11 0 0 1.293 1.293 0 0 0.97 0.97 3.592 2.694
12 12 0 0 0.776 0.776 0 0 0.582 0.582 2.155 1.616
13 13 0 0 0.466 0.466 0 0 0.349 0.349 1.293 0.97
14 14 0 0 0.279 0.279 0 0 0.209 0.209 0.776 0.582
15 15 0 0 0.168 0.168 0 0 0.126 0.126 0.466 0.349
16 16 0 0 0.101 0.101 0 0 0.075 0.075 0.279 0.209
17 17 0 0 0.06 0.06 0 0 0.045 0.045 0.168 0.126
18 18 0 0 0.036 0.036 0 0 0.027 0.027 0.101 0.075
19 19 0 0 0.022 0.022 0 0 0.016 0.016 0.06 0.045
20 20 0 0 0 0 0 0 0 0 0 0


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