1. Modified Rational Method
Storm Water Runoff
Modified Rational Method
Norman W. Garrick
CE 4410 Spring Lecture 12

2. Rational Method Used to estimate PEAK rate of runoff
From small drainage areas (< 200 acres)
1 acre = 43,560 sq. feet
1 acre is slightly smaller than a football field

3. Peak Rate of Runoff
Peak rate of runoff is used to design features that are
CARRYING water
Such as culverts, channels, swales, pipes

4. Total Runoff Volume
Total runoff volume is used to design features that are
Storing or Retaining water
Such as rain gardens, retention or detention ponds

5. Hydrographs A 20 minute hydrograph Is for a storm 20 minutes long
Each hydrograph is
associated with
a certain storm duration
A 20 minute hydrograph
Is for a storm 20 minutes long
Rate of runoff
Maximum for Hydrograph A
Maximum for Hydrograph B
Time

6. Hydrographs Rate of runoff Time Maximum for Hydrograph A
Area under hydrograph = total runoff volume

7. Modified Rational Method
The Rational Method is used to estimate PEAK rate of runoff
The Modified Rational Method estimates a bit more information
It is used to produce a simplified HYDROGRAPH for a storm
A hydrograph is a graph of rate of runoff versus time

8. Modified Rational Method
q = CCaiA
q = peak runoff rate (cu. feet per second)
C = runoff coefficient (between 0 and 1)
Ca = antecedent precipitation factor
i = rainfall intensity (inches per hour) for the design storm frequency
and the duration of the storm
A = area of drainage area (acres)
The antecedent precipitation factor is added to account for the fact that during a long storm event the ground will be saturated and will not be able to absorb more water
Note: CCa is never greater than 1.0

9. Recommended Antecedent Precipitation Factor
Storm Frequency Ca
2 to 10
1.0 25
1.1 50
1.2
100
1.25

10. Modified Rational Method Hydrographs
The Modified Rational Method is based on three types of hydrographs
Type A, Type B and Type C hydrographs
Type A Hydrograph: Storm Duration = Time of Concentration
Type B Hydrograph: Storm Duration > Time of Concentration
Type C Hydrograph: Storm Duration < Time of Concentration
MMR is recommended for very small drainage areas (< 20 acres)

11. Type A Hydrograph Storm Duration = Time of Concentration
Rate of runoff
qp = CCaiA
i is based on duration of storm
DUR qp Tc
Trec
Time

12. Type B Hydrograph Storm Duration > Time of Concentration
qmax = CCaiA
i is based on duration of storm
Rate of runoff
DUR
qmax Tc
Trec
Time

13. Type C Hydrograph Storm Duration < Time of Concentration
qmax = CCaiA(DUR/Tc)
i is based on duration of storm
DUR
qmax Tc
DUR
Time

14. Creating Hydrographs Example
Develop 10-, 25-, and 50-minute hydrographs for a 15 acres drainage area,
with C-value of 0.3 and a time of concentration of 25 minutes.
A 100-year frequency is desired

15. 10-minute Hydrograph
Duration = 10 minutes, Time of Concentration = 25 minutes
DUR < Tc, therefore, we need Type C Hydrograph

16. 10-minute Hydrograph Type C
qmax = CCaiA(DUR/Tc)
i is based on duration of storm
DUR = 10 min
qmax
Tc = 25 min
DUR = 10 min
Time

17. 10-minute Hydrograph Type C
qmax = CCaiA(DUR/Tc)
i is based on duration of storm
C = 0.3
Ca = 1.25
i: Return period = 100 year
Duration = 10 minutes
Figure 12.2
i = 7.9 iph
A = 15 acres
qmax = 0.3*1.25*7.9*15*(10/25) = 17.8 cfs
Time
10 min
qmax
25 min
35 min

18. 25-minute Hydrograph
Duration = 25 minutes, Time of Concentration = 25 minutes
DUR = Tc, therefore, we need Type A Hydrograph

19. 25-minute Hydrograph Type A
qmax = CCaiA
i is based on duration of storm
Rate of runoff
DUR = 25 qp
Tc = 25
Trec = 25
Time

20. 25-minute Hydrograph Type A
qp = CCaiA
i is based on duration of storm
C = 0.3
Ca = 1.25
i: Return period = 100 year
Duration = 25 minutes
Figure 12.2
i = 5.1 iph
A = 15 acres
qp = 0.3*1.25*5.1*15 = 28.7 cfs
Time 25 qp 50

21. 50-minute Hydrograph
Duration = 50 minutes, Time of Concentration = 25 minutes
DUR > Tc, therefore, we need Type B Hydrograph

22. 50-minute Hydrograph Type B
qmax = CCaiA
i is based on duration of storm
DUR = 50
qmax
Tc = 25
Trec = 25
Time

23. 50-minute Hydrograph Type B
qmax = CCaiA
i is based on duration of storm
C = 0.3
Ca = 1.25
i: Return period = 100 year
Duration = 50 minutes
Figure 12.2
i = 3.4 iph
A = 15 acres
qp = 0.3*1.25*3.4*15 = 19.1 cfs
Time 25
qmax 50 75