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HMR52: Probable Maximum Storm Computation (Eastern U.S.)

VERSION/DATE: April 1991




HMR52: Probable Maximum Storm Computation (Eastern U.S.) Users Manual March 1984 U.S. Army Corps of Engineers Water Resources Support Center The Hydrologic Engineering Center

HYDROMETEOROLOGICAL REPORT NO. 51 Probable Maximum Precipitation Estimates, United States East of the 105th Meridian June 1978 Prepared by Louis C. Schreiner and John T. Riedel Hydrometeorological Branch Office of Hydrology National Weather Service

NOAA HYDROMETEOROLOGICAL REPORT NO. 52 Application of Probable Maximum Precipitation Estimates - United States East of the 105th Meridian Prepared by E.M. Hansen, L. C. Schreiner & J.F. Miller Hydrometeorological Branch Office of Hydrology National Weather Service August 1962


HYDROMETEOROLOGICAL REPORT NO. 49 Probable Maximum Precipitation Estimates - Colorado River and Great Basin Drainages Prepared by E. Marshall Hansen, Francis K. Schwas, and John T. Riedel Hydrometeorological Branch Office of Hydrology National Weather Service Silver Spring, Md. September 1977



SECTION I - HMR52: Probable Maximum Storm Computation (Eastern U.S.) Users Manual



*** SECTION I - HMR52: Probable Maximum Storm Computation (Eastern U.S.) Users Manual

Program Purpose

Computer program HMR52 computes basin-average precipitation for Probable Maximum Storms (PMS) in accordance with the criteria specified in Hydrometeorological Report No. 52 (National Weather Service, 1982). That Hydrometeorological Report (HMR) describes a procedure for developing a temporal and spatial storm pattern to be associated with the Probable Maximum Precipitation (PMP) estimates provided in Hydrometeorological Report No. 51, "Probable Maximum Precipitation Estimates - United States East of the 105th Meridian." The U.S. National Weather Service (NWS) has determined the application criteria in a cooperative effort with the U.S. Army Corps of Engineers and the U.S. Bureau of Reclamation.

This program, HMR52, is applicable only to the eastern U.S., and is Intended for areas of 10 to 20,000 Mi2. (HMR No. 52 also contains a 1-mi2, 1-hr PMP). A time interval as small as 5 minutes can be used for storm definition. Before using the HMR52 program, one should be thoroughly familiar with the procedures described in Hydrometeorological Report No. 52.

The generalized PMP maps of HMR No. 51 are stippled in two regions, indicating estimates may be deficient because of orographic influences. Major projects within the stippled area should be considered on a case-by- case basis and expert hydrometeorological guidance should be sought.

Data required for application of the HMR52 program are: X.Y coordinates describing the river basin and subbasin watershed boundaries; PMP from HMR No. 51 (NWS, 1978); and Storm orientation, size, centering, and timing.

The program computes the spatially averaged PMP for any of the subbasins or combinations thereof. The Probable Maximum Flood (PMF) can then be computed as the runoff from the PMS, using an appropriate precipitation-runoff program such as HEC-1 (Hydrologic Engineering Center, HEC, 1981). A typical application of HMR52 does not produce a PMS. The PMS is defined by the Corps of Engineers to be that storm which produces the PMF. Thus, the PMS can only be determined by computing (and maximizing) runoff. That is, the runoff characteristics of a watershed must be considered in PMF (and therefore PMS) development.

HMR No. 52 requires that a critical storm-area size, orientation, centering and timing be determined which produces the maximum precipitation. The HMR52 computer program will optimize the storm-area size and orientation in order to produce the maximum basin-average precipitation. The user must provide the desired centering although the centroid of the basin area is provided as a default option.

The user must specify the time distribution for that storm. Using that time distribution information, the HMR52 program will produce a data file containing the incremental basin-average precipitation values for every subbasin requested. That precipitation data file will subsequently be input to a rainfall-runoff model, such as HEC-1, for computation of the resulting flood. The user then analyzes the various storm variables and recomputes the floods in order to determine the storm which produces the maximum runoff. That storm and runoff are defined as the PMS and PMF, respectively.

Computer Requirements

The HMR52 computer program requires a computer with 45K (decimal) words of core storage and 7 scratch tape/disk files. Plots of the basin geometry and storm patterns can be made on a line printer. Section 10 of this manual specifies detailed computer hardware and software requirements.


The computer program HMR52 was written by Paul B. Ely of the HEC. John C. Peters provided much valuable assistance in the design of the program's capabilities and applications methodology.



Generalized estimates of Probable Maximum Precipitation, the greatest rainfall rates for specified durations theoretically possible, are presented for the United States east of the 105th meridian. They are all- season estimates, that is, the greatest for any time of year, for drainages from 10 to 20,000 mi2 (26 to 51,800 km2) for durations of 6 to 72 hours. Details of the procedures and methods used for developing these estimates are described.



Generalized charts setting the level of all-season Probable Maximum Precipitation (PMP) for drainages up to 1,000 mi2 (2,590 km2), covering the United States east of the 105th meridian, have been available since 1947- (U.S. Weather Bureau 1947) and the seasonal variation since 1956 (Riedel et al. 1956). These studies have been used extensively by the Corps of Engineers, other Federal agencies, State and local governments, private engineers and meteorologists. Because of increased interest in projects involving large drainages, it was found necessary to extend estimates to areas greater than 1,000 mi2 (2,590 km2). At the same time it was necessary to revise the small area, less than 1,000 mi2 (2,590 km2) study in order to appropriately consider all important historical storms; for example, the Yankeetown, Fla. storm of September 3-7, 1950. The areal depths for this storm were not available when the 1956 study was prepared.


Discussions concerning the need for the generalized PMP charts for large areas were held at a meeting with representatives of the Office of the Chief, Corps of Engineers, at Phoenix, Ariz., May 17-20, 1971. Authorization for the revision of the previous small-area study and coordination of the results with the extension to larger areas stemmed from a meeting with representatives of the Office of the Chief, Corps of Engineers at Silver Spring, Md., September 19, 1974.

Definition of PMP

PMP is defined as "the theoretically greatest depth of precipitation for a given duration that is physically possible over a particular drainage area at a certain time of year," (American Meteorological Society 1959). In consideration of our limited knowledge of the complicated processes and interrelationships in storms, PMP values are identified as estimates.

Another definition of PMP more operational in concept is "the steps followed by hydrometeorologists in arriving at the answers supplied to engineers for hydrological design purposes" (WMO 1973). This definition leads to answers deemed adequate by competent meteorologists and engineers and judged as meeting the requirements of a design criterion.


This study can be used to determine drainage average all-season PMP for any drainage from 10 to 20,000 mi2 (26 to 51,800 km2) in area for durations of 6 to 72 hours in the United States east of the 105th meridian. In northern portions of the region, all-season PMP may not yield the probable maximum flood. Critical spring soil conditions with snow on the ground, in combination with spring season PMP, values may yield greater flood peaks.

Generalized vs. Individual Drainage Estimates

The PMP values of this study are termed generalized estimates. By this we mean isolines of PMP are given on a map allowing determination of average PMP for any drainage.

Through the years, the Hydrometeorological Branch has determined PMP estimates for individual drainages. This was done: (a) if generalized PMP studies were not available, (b) for drainages larger in size than covered by available generalized PMP studies, or (c) for drainages such as in the Appalachians, where detailed studies indicated orographic effects would yield PMP estimates significantly different from those determined from available generalized PMP charts. Some of the more substantive studies have been published. The more recent ones cover drainages of the Red River of the North and Souris River (Riedel 1973), the Colorado and Minnesota Rivers (Riedel et al. 1969), the Tennessee River (Schwarz 1965, and Schwarz and Relfert 1969) and the Susquehanna River (Goodyear and Riedel 1965). These and other unpublished individual drainage PMP estimates made by the Hydrometeorological Branch may take precedence over estimates obtained from generalized PMP studies of this report because the individual drainage studies take into account orographic features that are smoothed out in this study. On the other hand, due to passage of time, individual drainage studies will not necessarily include recent storm data and advances in meteorological concepts. It is not practical to evaluate all the individual drainage PMP estimates at this time. We suggest a decision be made on a case-by-case basis as needed.

Stippled Regions on PMP Maps

The generalized PMP maps (figs. 18-47) are stippled in two regions, (a) the Appalachian Mountains extending from Georgia to Maine and (b) a strip between the 103rd and 105th meridian. This stippling outlines areas within which the generalized PMP estimates might be deficient because detailed terrain effects have not been evaluated.

In developing the maps of PMP, it was sometimes necessary to transpose storms to and from higher terrain. Determination of storm transposition limits (section 2.4.2) took into account topography homogeneity in a general sense, thereby avoiding major topographic considerations. However, regional analysis required definition across mountains such as the Appalachians. For such regions, the assumption was made that the reduced height of the column of moisture available for processing (section 2.3.2) at higher elevations is compensated by intensification from steeper terrain slopes.

In contrast to the use of these simplifying assumptions, studies of PMP covering portions of the Western States (U.S. Weather Bureau 1961, 1966, and Hansen et al. 1977) and the Tennessee River drainage (Schwarz and Helfert 1969) do take into account detailed terrain effects. A laminar flow orographic precipitation computation model, useful in some regions where cool-season precipitation is of greatest concern, gives detailed definition for some of the Western States. For the Tennessee River drainage, nonorographic PMP was adjusted for terrain effects by consideration of numerous different rainfall criteria, taking into account meteorological aspects of critical storms of record.

We expect future studies of the Hydrometeorological Branch will involve detailed generalized studies covering the stippled regions. Until these studies are completed, we suggest that major projects within the stippled regions be considered on a case-by-case basis as the need arises.

Application of Drainage PMP Values

The results of this study are drainage average PMP depths for the designated durations (6 to 72 hours) without specifying a time sequence for occurrence of 6-hr incremental PMP values. A companion report (Hansen and Schreiner) to this study covers methods for spatially distributing the most important 6-hr PMP increments. It also gives meteorological reasonable time sequences of the 6-hr PMP increments from the beginning of the PMP storm. Additionally, shape and orientation of isohyetal patterns are discussed.



This study provides a stepwise approach to the temporal and spatial distribution of probable maximum precipitation (PMP) estimates derived from Hydrometeorological Report No. 51, "Probable Maximum Precipitation Estimates - United States East of the 105th Meridian." Included are discussions of the shape and orientation of isohyetal patterns for major rainfalls of record. An elliptical isohyetal pattern with a ratio of major to minor axes of 2.5 to 1 is recommended, and a procedure is outlined for obtaining appropriate isohyet values. A procedure is given to determine PMP values for durations less than 6 hours. Example applications have been worked through to serve as guidance in the use of this procedure.



Generalized estimates of all-season probable maximum precipitation (PMP) applicable to drainages of the United States east of the 105th meridian are provided in Hydrometeorological Report No. 51 (Schreiner and Riedel 1978). Hereinafter, that report will be referred to as HMR No. 51, and references to other reports in this series will be similarly abbreviated.

The terminology in HMR No. 51 has not always been precise, particularly where PMP estimates are referred to as being for drainages from 10 to 20, 000 mi2. It is important to realize that the term drainages as used in that report is a rather loose interpretation when the more precise term is areas. The term drainage or drainage area in the present report will apply to a specific drainage only. HMR No. 51 provides storm-area PMP estimates for a specific range of area sizes (10 to 20,000 mi2) and durations (6 to 72 hr).


The objective of this report is to aid the user in adapting or applying PMP estimates from HMR No. 51 to a specific drainage. This report recommends a procedure for the application of PMP estimates to a drainage for which both the temporal and spatial distributions are needed. This information is necessary for the determination of peak discharge and can be useful in estimating the maximum volume in evaluations of the probable maxim flood (PMF).


PROBABLE MAXIMUM PRECIPITATION (PMP). Theoretically the greatest depth of precipitation for a given duration that is physically possible over a given size storm area at a particular geographical location at a certain time of the year. (This definition is a 1982 revision to that used previously (American Meteorological Society 1959) and results from mutual agreement- among the National Weather Service, the U.S. Army Corps of Engineers, and the Bureau of Reclamation.)

PMP STORM PATTERN. The isohyetal pattern that encloses the PMP area plus the isohyets of residual precipitation outside the PMP portion of the pattern.

STORM-CENTERED AREA-AVERAGED PMP. The values obtained from HMR No. 51 corresponding to the area of the PMP portion of the PMP storm pattern. In this report all references to PMP estimates or to incremental PMP infer storm-area averaged PMP.

DRAINAGE-AVERAGED PMP. After the PMP storm pattern has been distributed across a specific drainage and the computational procedure of this report applied, we obtain drainage-averaged PMP estimates. These values include that portion of the PMP storm pattern that occur over the drainage, both PMP and residual.

TEMPORAL DISTRIBUTION. The order in which 6-hr incremental amounts are arranged in a 3-day sequence (72 hr). This report includes information regarding determination of hourly and smaller units within the maximum 6-hr increment, but does not discuss the distribution of units less than 6-hr.

SPATIAL DISTRIBUTION. The value of fixed isohyets in the idealized pattern storm for each 6-hr increment and shorter durations within the maximum 6-hr increment of PMP when area-averaged PMP is to be distributed.

TOTAL STORM AREA AND TOTAL STORM DISTRIBUTION. The largest area size and longest duration for which depth-area-duration data are available in the records of major storm rainfall.

STANDARD AREAS. The specific area sizes for which PMP estimates are available from the generalized 2 maps in HMR No. 51, i.e., 10-, 200-1 19000-1 5,000-, 10,000-, and 20,000--mi2 areas.

STANDARD ISOHYET AREA SIZES. In this report, the standard isohyet area sizes are those enclosed by the isohyets. of the. recommended pattern, i.e., 10, 25, 50, 100, 175, 300, 450, 700, 1,000,,,1,500, 2,150, 3,000, 4,500, 6,500, 10,000, 15,000, 25,000, 40,000, and 60,000 mi2.

RESIDUAL PRECIPITATION. The precipitation that occurs outside the area of the PMP pattern placed on the drainage, regardless of the area size of the drainage. Because of the irregular shape of the drainage, or because of the choice of a PMP pattern smaller in area than the area of the drainage, the residual precipitation can fall within the drainage. A particular advantage in the consideration of residual precipitation, is that of allowing for the determination of concurrent precipitation, i.e., the precipitation falling on an adjacent drainage as compared to that for which the PMP pattern has been applied.

ISOHYETAL ORIENTATION. The orientation (direction from north) of the major axis through the elliptical pattern of PMP. The term is used in this study also to define the orientation of precipitation patterns of major storms when approximated by elliptical patterns of best fit.

WITHIN/WITHOUT-STORM DEPTH-AREA RELATIONS. This relation evolves from the concept that the depth-area relation for area-averaged PMP represents an envelopment of maximized rainfall from various storms each effective for a different area size(s). The within-storm depth-area relation represents the areal variation of precipitation within a storm that gives PMP for a particular area size. This can also be stated as the storm that results in PMP for one area size my not give PMP for any other area size. Except for the area size that gives PMP, the within-storm depth-area relation will give depths less than PMP for smaller area sizes. This concept is illustrated in the schematic diagram shown in figure 1. In this figure, precipitation for areas in the PMP storm outside the area size of the PMP pattern describes a without-storm depth-area relation. The precipitation described by the without-storm relations is the residual precipitation defined elsewhere in this report.

Summary of Procedures and Methods of this Report

All procedures described in this study are based on information derived from major storms of record, and are applicable to nonorographic regions of the eastern United States.

The temporal distributions provided allow some flexibility in determining the hydrologically most critical sequence of incremental PMP. The procedure used to determine the temporal distributions has been used in some other Hydrometeorological Branch reports (Riedel 1973, and Schwarz 1973 for example), and is described in chapter 2.

We have surveyed major storm isohyetal patterns for statistics on pattern shape, and have adopted an elliptical shape having a 2.5 to 1 ratio of major to minor axes as representative of a precipitation pattern. This elliptical shape has been adopted for PMP and is applied to all 6-hr incremental patterns. The discussion of the shape of the isohyetal patterns is found in chapter 3.

Another aspect of this study is a generalized approach to adjustments for pattern orientation to fit the drainage when inconsistent with the orientation determined for the PMP isohyetal pattern. Outlined in chapter 4 is an empirical method that allows up to 15 percent reduction to storm- centered area-averaged PMP for drainage areas larger than 3,000 mi2 which differ by more than 40 degrees from the orientation consistent with PMP- producing storms.

In determining spatial distribution a basic assumption is that rainfall depths for areas smaller and larger than the total area for which PMP is needed over a particular drainage, are less than PMP. (See within/without- storm depth-area definitions.) This assumption, for areas smaller than the PMP, has been commonly made in some other studies by this branch (Riedel 1973, Riedel, et al. 1969, and others), and results in what has been referred to in those reports as within-storm or within-drainage depth-area- duration (D.A.D) relations. Application of a similar assumption to areas larger then for the PMP is a consideration unique to the present study and introduces the concept of residual precipitation.

For many drainages, it is frequently necessary to have values for durations less than 6 hours. Procedures for obtaining the percentage of the greatest 6-hr increment that occurs in the maximum 5, 15, 30 and 60 min are provided in chapter 6. We do not in this report attempt to define the temporal distribution within the greatest 6-hr increment except to suggest that the 5-, 15- and 30-min values should be included within the maximum 60 sin. It is anticipated that the time of occurrence of the maximum 60 min within the 6-hr increment will be the subject of a future study.

Application to PMP

For those interested in the application of PMP from HMR No. 51 (nonorographic region only) to a specific drainage, chapter 7 is most important. This chapter provides a step-by-step approach to guide the user through the application of procedures developed in this report. Examples have been worked out in sufficient detail to clarify important aspects of these procedures.

The examples in chapter 7 give the user a procedure to obtain the maximum volume of rainfall for a drainage. Finding the maximum volume of rainfall is only part of the hydrologic problem. Another important question is the probable maximum peak flow that could occur at the proposed hydrologic structure. The solution is somewhat more difficult to directly ascertain than finding the maximum volume. The calculation of peak flow is highly dependent on a mixture of basin parameters such as lag time, time of concentration, travel time, and loss rate functions in combination with the amount, distribution and placement of the PMP storm within the drainage. Because of the interaction of these parameters, we cannot provide a simple stepwise procedure to determine peak flow. The user must weigh carefully the effect of the various parameters, drawing on his experience and knowledge of the drainage under study, and determine, through a series of trials, what combination of hydrologic parameters will produce the maximum peak flow.

Some Other Aspects of Temporal and Spatial Distributions

Although we present a procedure that leads to temporal and spatial distribution of PMP, we recognize that some considerations have not been discussed in this study. When storm data become sufficiently plentiful, and when our knowledge of storm dynamics permits, these considerations my lead to improvements in the current procedures. Meanwhile only brief comments follow regarding two such considerations for future study.

Moving Rainfall Centers

Our procedure assumes that isohyetal patterns for all 6-hr PMP increments remain fixed with time, i.e., all are, centered at the same location. For large drainages (greater than 10,000 mi2, for example), it is meteorologically reasonable for the rainfall center to travel across the drainage with time during the storm. It is conceivable that such movement could result in a higher flood peak if the direction and speed of movement coincides with downstream progression of the flood crest.

It was decided jointly by the Corps of Engineers and the Hydrometeorological Branch that the present report would not cover application of moving centers. Generalization of moving centers would require analysis of observational data such as incremental storm isohyetal patterns that are presently not available. It is anticipated that a future study will cover moving centers.

Distributions From An Actual Storm

Use of elliptical patterns for spatial distribution permits simplicity in generalized depth-area relations and in determining isohyet values. It also helps maintain consistency in results among drainages, area sizes, and durations. Such consistency is also maintained by the recommended temporal distributions. An alternate but unrecommended procedure is to adopt the distributions of a record storm precipitation that occurred on the drainage or within a homogeneous region including the drainage.

The isohyetal pattern from an actual storm might "fit" a drainage better than an elliptical pattern, and multiplying the isohyets by percent of PMP (say for 6 hours for the drainage, divided by the drainage depth from the storm pattern after it is located on the drainage) will give isohyet values for PMP. Such isohyets, however, quite possibly could give greater than PMP depths for smaller areas within the drainage.

The temporal distribution of such a storm could also be used for PMP. Again, however, there could very likely be problems. The most intense three 6-hr rain increments in a 72-hr storm may be widely separated in a time sequence of incremental rainfall (mass curve). Thus, 12- or 18-hr PMP could not be obtained unless rain bursts somehow were brought together. However, such arrangement is often done as a maximization step and PMP depths from HMR No. 51 used. These modifications would be towards the generalized criteria of the present study in which there are no results that are inconsistent or irreconcilable.

Paulhus and Gilman (1953) published a technique for using an actual pattern for, distributing PMP. The referenced paper describes a "sliding" technique for obtaining the spatial distribution of PMP that has its greatest merit in applications in the more orographic regions (stippled zones in HMR No. 51) covered by this study, such as the Appalachians and along the western border to the region, where site-specific studies are recommended.' However, we advise caution in application of this technique directly as Paulhus and Gilman have proposed, in that it is possible to obtain PMP for a much smaller area size than that for the drainage to which it is applied. Since this disagrees with our within-storm concept, we therefore suggest adherence to the following modifications to the technique presented by Paulhus and Gilman, if it is used:

a. Use a set of depth-area relations (from HMR No. 51) which, when "slid over" the depth-area relations for the storm, will give PMP for an area size within 10 percent of the area of the drainage of concern.

b. It is desirable that PMP (from HMR No. 51) be obtained for at least the hydrologically critical duration.

c. For other durations between 6 and 72 hours, stay within 15 percent of PMP as specified in HMR No. 51. For additional information regarding application of this technique, the reader is referred to the Paulhus and Gilman paper.

Other Meteorological Considerations

Other aspects of extreme rainfall criteria can be important to determinations of peak flow. Some of these aspects are described here.

PMP For Smaller Areas Within The Total Drainage.

Our previous studies have concentrated on defining PMP for the total drainage area. In fact, in the present study we recommend spatial distributions resulting in somewhat less than PMP for smaller as well as larger areas than the PMP pattern., The question can naturally be asked, does PMP for a smaller area size than the storm area size that is applicable to the entire drainage, which when centered over a portion of the drainage (experiencing more intense rainfall than that for the entire drainage), result in a more critical peak flow? There is a possibility that PMP covering only a subportion of the drainage could provide a hydrologically more critical peak discharge, and the hydrologist should consider such a possibility. The depth of rainfall to use over the remaining portion of the drainage would need to be specified. (See discussion on residual precipitation in sections 3.5.3 and 5.2.5.)

Rains For Extended Periods

Especially for large drainages, rainfalls for durations longer than 3 days could be important in defining critical volumes for hydrologic design. As examples, the Hydrometeorological Branch, working with Corps of Engineers hydrologists, has evaluated the meteorology of hypothetical sequences of record storms transposed in space and recommended how close together such storms can follow each other (Myers 1959, and Schwarz 1961). Similar studies may be needed for other-large drainage projects. Sufficiently severe assumptions, however, relative to how full reservoirs are prior to the PMF and the antecedent soil conditions, could obviate the need for such studies.

Report Preparation

Preparation of this report began in 1977 as follow on studies to HMR No. 51. Initial discussions with the Corps of Engineers outlined the scope of the project. As indicated in a previous section, certain problems were left to be considered in later studies. The basic studies were undertaken when all the authors were affiliated with the National Weather Service (NWS). These studies were completed after one of the authors, L. Schreiner, transferred to the Bureau of Reclamation (USBR). Several of the concepts and procedures included in this report evolved after Mr. Schreiner's transfer, as a collaborative effort of the three authors and other meteorologists affiliated with both the NWS and the USBR.
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