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

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

PMP Development Timeline 1970s-Present: PMP is formalized and becomes standard of practice 1920 -1950: 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

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 100 for many areas

Creager Envelop Curve

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

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

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.

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

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

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

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

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

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.

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

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.

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.

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”