1. History and Evolution of the PMP/PMF
David F. Kibler and Michael Bliss
Civil and Environmental Engineering
Virginia Tech

2. PMP and PMF Definitions
PMP – Probable Maximum Precipitation:
“theoretically, the greatest depth of precipitation for a given duration that is physically possible over a given size storm area at a particular geographic location during a certain time of year”
PMF – Probable Maximum Flood:
“the flood that may be expected from the most severe combination of critical meteorologic and hydrologic conditions that are reasonably possible in the drainage basin under study”
Source: FEMA Interagency Committee on Dam Safety, Oct., 1998

3. PMP Development Timeline
1970s-Present: PMP is formalized and becomes standard of practice
: Flood prediction linked to storm precipitation
1910 – 1940: Hydrology methods begin to emerge
Time Periods
1900
1950
2000
Pre-1900: No consistent data from U.S. Weather Bureau – used “worst known flood”
1953: Yarnell publishes rainfall intensity charts for U.S.
Key Events
1978: HMR 51,52 is published; PMP east of 105th Meridian
1950: Creager and Justin develop “Creager” envelop curve equation
1961: Tech. Paper 40 links storm recurrence to depth of precipitation
By 1930: Formal statistical methods are applied to hydrologic problems
1942: C.S. Jarvis develops “Myers” envelope curve equation

4. Popular Maximum Discharge Formulas of the 1940-60s
Myers Equation (C.S. Jarvis, 1942)
Q = 10,000A0.5
where A = drainage area, sq. miles for watersheds
larger than 4 sq. miles
Q = ultimate maximum flood flow (cfs)
Creager Equation (Creager and Justin, 1950)
Q = 46CA(0.894A-0.048)
where C = coefficient with maximum value of for many areas

5. Creager Envelop Curve

6. PMP Timeline (cont.)
1998: FEMA publishes procedure for selecting inflow design floods – introduces “acceptable incremental consequences” for selecting design floods
By 1970: All federal agencies use PMP estimation for spillway design
1970
1980
1990
2000
1988: ASCE Task Committee proposed 3 hazard categories: Cat 1 (high) = PMP Cat 2 (medium) = PMF or smaller base on risk analysis Cat 3 (low) = Q10 – Q100
1985: NRC’s Dam Safety criteria stated it would be acceptable for non-PMP design on certain projects
1973: ASCE Task Committee proposes an alternative approach to PMP – economic analysis of risk
1979: Published Fed. Dam Safety guidelines acknowledged risk analysis, but favored PMP methods
1986: FEMA workgroup favored PMP, but gave guidance that Federal Agencies could develop agency specific criteria

7. PMP vs. Extreme Rainfall Events
Source: “PMPs Never Happen – or Do They?” (Harrison, 2002)

8. Do actual observed rainfalls ever approach the PMP?
The Mid-Atlantic Region has experienced three of the top five most intense 12-hr storms in US.
At Smethport, PA (1942), the PMP was exceeded by 19%.
The other two occurred in VA and approached 81 and 86% (Madison County, 1995) of PMP for areas less than 10 mi2.
See Fig. 5, Harrison, 2002.

9. Heaviest 12-Hr Rainfalls
Source: “PMPs Never Happen – or Do They?” (Harrison, 2002)

10. Do actual floods ever approach the PMF?
Harrison and Paxson have developed Fig. 6 for floods in the Northern Appalachian area (PA).
The PMFs lie above the envelop curve for maximum observed floods in PA.
See Fig. 6

11. Northern Appalachian Region
Source: “Ballpark PMFs” (Harrison, 2004)

12. Central Appalachian Region
However, for the Central Appalachian region, the PMF
curve is very close to the envelop line representing the
most severe observed (historical) floods on record for
the area
See Fig. 7 from Harrison and Paxson, 2004

13. Central Appalachian Region
Source: “Ballpark PMFs” (Harrison, 2004)

14. Recent PMF Relationships
Using data from PA, Harrison and Paxson (2002) developed statistical relationships for the PMF, the best of which is:
Q = 8148A0.69
where Q = est. PMF in cfs; A = drainage area, sq mi
Looks a lot like the old Myers equation -- we have come full-circle!
But -- statistical PMF relations intended only for checking purposes in areas where there is little hydrologic data available. See Fig 7. Harrison and Paxson.

15. PMF vs. Drainage Areas
Source: “Ballpark PMFs” (Harrison, 2003)

16. Summary and Current Status of PMP/PMF
The PMP and PMF concepts have been with us for at least 50 years and perhaps longer.
The PMF has been recognized as a standard of practice since about 1970.
We have experienced near-PMPs in mid-Atlantic states.
However, there remain uncertainties regarding the estimation of the PMP, its time distribution and its probability of occurrence.

17. Summary and Current Status of PMP/PMF (cont.)
PMFs in the southern mid-Atlantic are seen to approach the envelop of observed maximum (historical) floods.
Nevertheless, questions remain about the PMF, because it is a hydrologic estimate based on the PMP and the saturation condition of the watershed.

18. Summary and Current Status of PMP/PMF (cont)
Because it has almost zero exceedance probability, the PMF is difficult to fit into current-day risk analysis
The use of fractional parts of the PMF has led to an inconsistent standard across US
Other approaches have been adopted, such as the use of “incremental analysis”