History and History and Evolution of the Evolution of the

PMP/PMFPMP/PMFDavid F. Kibler and Michael David F. Kibler and Michael

BlissBliss

Civil and Environmental Civil and Environmental EngineeringEngineering

Virginia TechVirginia Tech

PMP and PMF DefinitionsPMP and PMF Definitions

PMP – Probable Maximum Precipitation: PMP – Probable Maximum Precipitation:

““theoretically, the greatest depth of precipitation for theoretically, the greatest depth of precipitation for a given duration that is physically possible over a a given duration that is physically possible over a given size storm area at a particular geographic given size storm area at a particular geographic location during a certain time of year” location during a certain time of year”

PMF – Probable Maximum Flood:PMF – Probable Maximum Flood:

““the flood that may be expected from the most the flood that may be expected from the most severe combination of critical meteorologic and severe combination of critical meteorologic and hydrologic conditions that are reasonably possible in hydrologic conditions that are reasonably possible in the drainage basin under study”the drainage basin under study”

Source: FEMA Interagency Committee on Dam Safety, Source: FEMA Interagency Committee on Dam Safety, Oct., 1998Oct., 1998

By 1930: Formal statistical methods are applied to hydrologic problems

1953: Yarnell publishes rainfall intensity charts for U.S.

1910 – 1940: Hydrology methods begin to emerge

1900 1950 2000

1920 -1950: Flood prediction linked to storm precipitation

1942: C.S. Jarvis develops “Myers” envelope curve equation

1970s-Present: PMP is formalized and becomes standard of practice

1978: HMR 51,52 is published; PMP east of 105th Meridian

1961: Tech. Paper 40 links storm recurrence to depth of precipitation

PMP Development TimelineT

ime

Per

iod

sK

ey E

ven

ts Pre-1900: No consistent data from U.S. Weather Bureau – used “worst known flood”

1950: Creager and Justin develop “Creager” envelop curve equation

Popular Maximum DischargePopular Maximum DischargeFormulas of the 1940-60sFormulas 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 CurveCreager Envelop Curve

PMP Timeline (cont.)PMP Timeline (cont.)

1970 1980 20001990

By 1970: All federal agencies use PMP estimation for spillway design

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

1985: NRC’s Dam Safety criteria stated it would be acceptable for non-PMP design on certain projects

1986: FEMA workgroup favored PMP, but gave guidance that Federal Agencies could develop agency specific criteria

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

1998: FEMA publishes procedure for selecting inflow design floods – introduces “acceptable incremental consequences” for selecting design floods

PMP vs. Extreme Rainfall EventsPMP vs. Extreme Rainfall Events

Source: “PMPs Never Happen – or Do They?” (Harrison, 2002)

Do actual observed rainfalls ever Do actual observed rainfalls ever approach the PMP?approach the PMP?

The Mid-Atlantic Region has The Mid-Atlantic Region has experienced three of the top five experienced three of the top five most intense 12-hr storms in US. most intense 12-hr storms in US.

At Smethport, PA (1942), the PMP At Smethport, PA (1942), the PMP was exceeded by 19%. was exceeded by 19%.

The other two occurred in VA and The other two occurred in VA and approached 81 and 86% (Madison approached 81 and 86% (Madison County, 1995) of PMP for areas County, 1995) of PMP for areas less than 10 miless than 10 mi22. .

See Fig. 5, Harrison, 2002See Fig. 5, Harrison, 2002. .

Heaviest 12-Hr RainfallsHeaviest 12-Hr Rainfalls

Source: “PMPs Never Happen – or Do They?” (Harrison, 2002)

Do actual floods ever Do actual floods ever approach the PMF?approach the PMF?

Harrison and Paxson have developed Harrison and Paxson have developed Fig. 6 for floods in the Northern Fig. 6 for floods in the Northern Appalachian area (PA). Appalachian area (PA).

The PMFs lie above the envelop The PMFs lie above the envelop curve for maximum observed floods curve for maximum observed floods in PA. in PA.

See Fig. 6See Fig. 6

Northern Appalachian RegionNorthern Appalachian Region

Source: “Ballpark PMFs” (Harrison, 2004)

Central Appalachian RegionCentral Appalachian Region

However, for the Central Appalachian However, for the Central Appalachian region, the PMFregion, the PMFcurve is very close to the envelop line curve is very close to the envelop line representing the representing the most severe observed (historical) floods most severe observed (historical) floods on record for on record for the areathe area

See Fig. 7 from Harrison and Paxson, See Fig. 7 from Harrison and Paxson, 20042004

Central Appalachian RegionCentral Appalachian Region

Source: “Ballpark PMFs” (Harrison, 2004)

Recent PMF RelationshipsRecent PMF Relationships

Using data from PA, Harrison and Paxson Using data from PA, Harrison and Paxson (2002) developed statistical relationships for (2002) developed statistical relationships for the PMF, the best of which is:the PMF, the best of which is: Q = 8148AQ = 8148A0.69 0.69

where Q = est. PMF in cfs; A = drainage where Q = est. PMF in cfs; A = drainage area, sq miarea, sq mi

Looks a lot like the old Myers equation -- we Looks a lot like the old Myers equation -- we have come full-circle! have come full-circle!

But -- statistical PMF relations intended only But -- statistical PMF relations intended only for checking purposes in areas where there is for checking purposes in areas where there is little hydrologic data available. See Fig 7. little hydrologic data available. See Fig 7. Harrison and Paxson.Harrison and Paxson.

PMF vs. Drainage AreasPMF vs. Drainage Areas

Source: “Ballpark PMFs” (Harrison, 2003)

Summary and Current StatusSummary and Current Status of PMP/PMF of PMP/PMF

The PMP and PMF concepts have been The PMP and PMF concepts have been with us for at least 50 years and perhaps with us for at least 50 years and perhaps longer. longer.

The PMF has been recognized as a The PMF has been recognized as a standard of practice since about 1970. standard of practice since about 1970.

We have experienced near-PMPs in mid-We have experienced near-PMPs in mid-

Atlantic states.Atlantic states.

However, there remain uncertainties However, there remain uncertainties regarding the estimation of the PMP, its regarding the estimation of the PMP, its time distribution and its probability of time distribution and its probability of occurrence.occurrence.

PMFs in the southern mid-Atlantic are PMFs in the southern mid-Atlantic are seen to approach the envelop of seen to approach the envelop of observed maximum (historical) floods. observed maximum (historical) floods.

Nevertheless, questions remain about Nevertheless, questions remain about the PMF, because it is a hydrologic the PMF, because it is a hydrologic estimate based on the PMP and the estimate based on the PMP and the saturation condition of the watershed.saturation condition of the watershed.

Summary and Current StatusSummary and Current Status of PMP/PMF (cont.) of PMP/PMF (cont.)

Summary and Current StatusSummary and Current Status of PMP/PMF (cont) of PMP/PMF (cont)

Because it has almost zero exceedance Because it has almost zero exceedance probability, the PMF is difficult to fit into probability, the PMF is difficult to fit into current-day risk analysiscurrent-day risk analysis

The use of The use of fractional partsfractional parts of the PMF of the PMF has led to an inconsistent standard has led to an inconsistent standard across USacross US

Other approaches have been adopted, Other approaches have been adopted, such as the use of “incremental analysis”such as the use of “incremental analysis”